The Crusades, wars by European Christians against the Muslims world are sometimes confused with early Islamic Conquests of 7th Century CE, when Muslims fought against their contemporary rivals including Christian Byzantine Empire. Unfortunately, some even ignorantly claim "Muslims attacked Christians first" and that resulted in Crusades of 11 Century CE. Despite the fact that the Papal Authority of 11th Century did use the Islamic Conquests as a pretext to launch Crusades yet there is a huge difference between the Crusades and the wars Muslim armies fought against their regional rivals. As per dictionary.com the term "Crusades" is defined as "any of the military expeditions undertaken by the Christians of Europe in the 11th, 12th, and 13th centuries for the recovery of the Holy Land from the Muslims." The Muslim attacks against Byzantine Christian Empire was not based on religious zeal to fight Christian faith where as Crusades were particularly waged with a mindset to eliminate Islam and Muslims especially from the Holy Land and its precincts. The following three major differences between Crusades and Early Islamic Conquests discussed further will clarify this topic.
Firstly the crusades were specifically aimed at getting rid of Islam and Muslims from the Holy Land of Jerusalem and its adjoining areas while Muslim armies attacking Christian Byzantine empire did not do so with this aim. The main reason that Muslim armies battled Byzantine Empire was because the former's emergence as a new regional power brought them face to face in a war situation with 2 hostile regional neighbors: Sassanian Empire and the Byzantine Empire. Before Islam these 2 main regional powers were already at war with each other for centuries for the control of entire region, please read Roman–Persian Wars. After the acceptance of Islam the Arabs gained strength in the Arabian Peninsula and sooner or later the armies of these 2 empires that could not stand each other were naturally not going to accept a third upcoming power in their neighborhood. In fact the showdown of Muslims with these 2 empires was already inevitable when they displayed hostility to Prophet Muhammad's emissaries. Khusrow Pervez - Khusrow II (Chosroes II) the then Sassanian Ruler after receiving the Prophet's letter "tore the letter into shreds and forthwith dictated a command to his viceroy in Yemen to send a couple of troopers to arrest the Prophet and bring him to his presence." The first conflict between Muslims and Byzantine empire happened in Battle of Mu'tah. This happened as a result of an emissary that Prophet Muhammad ﷺ sent to ruler of Bosra, in modern day Syria, and on his way, he was intercepted and killed by al-Ghassani, a Christian Arab governor and a close ally to the Byzantine Emperor Heraclius (ruled 610 to 641 CE). Killing a peace emissary was considered an act of war. This led towards the famous Expedition of Tabuk led by Prophet Muhammad ﷺ himself to show a force of strength to the Byzantines. Such incidents led the Muslims towards wars with their hostile neighbors that included not only Christians but also the fire worshiping Magians of Sassanian empire.
Secondly and most importantly for many Christians who may not know, especially in the mainstream West, that when Arab Muslim armies were fighting Byzantine, the Christians of the region in many cases sided with the Muslims due to obvious reasons that Muslims were not waging a sort of a Crusade against people of other faiths. They were in fact seen as a liberating force against the Byzantine and Persian oppression. This can be confirmed from the words of the Christian Priests and religious leaders of early Islamic history. T. W. Arnold writes in his Preaching of Islam:
"Michael the Elder, Jacobite Patriarch of Antioch, writing in the latter half of the twelfth century, could approve the decision of his co-religionists and see the finger of God in the Arab conquests even after the Eastern churches had had experience of five centuries of Muhammadan rule. After recounting the persecutions of Heraclius, he writes: "This is why the God of vengeance, who alone is all-powerful, and changes the empire of mortals as He will, giving it to whomsoever He will, and uplifting the humble — beholding the wickedness of the Romans who, throughout their dominions, cruelly plundered our churches and our monasteries and condemned us without pity — brought from the region of the south the sons of Ishmael, to deliver us through them from the hands of the Romans. And, if in truth, we have suffered some loss, because the catholic churches, that had been taken away from us and given to the Chalcedonians, remained in their possession; for when the cities submitted to the Arabs, they assigned to each denomination the churches which they found it to be in possession of (and at that time the great church of Emessa and that of Harran had been taken away from us); nevertheless it was no slight advantage for us to be delivered from the cruelty of the Romans, their wickedness, their wrath and cruel zeal against us, and to find ourselves at peace."
T. W. Arnold mentions another incident when Muslim armies under Abu Ubayda (r.a), a companion of Prophet Muhammad ﷺ, reached the valleys of Jordan and took control of the area, the Christians welcome them with open arms due to the kind treatment of their non-Muslim subjects for which they were well known. The writer says: “When the Muslim army reached the valley of the Jordan and Abu Ubaydah pitched his camp at Fiḥ l, the Christian inhabitants of the country wrote to the Arabs, saying: "O Muslims, we prefer you to the Byzantines, though they are of our own faith, because you keep better faith with us and are more merciful to us and refrain from doing us injustice and your rule over us is better than theirs, for they have robbed us of our goods and our homes." The people of Emessa closed the gates of their city against the army of Heraclius and told the Muslims that they preferred their government and justice to the injustice and oppression of the Greeks.”
In many cases Arab Christian tribes sided with the Muslim armies, such as Banu Taghlib, assisted Muslims in their battles against Persian armies and retained their Christian identity under the Muslim rule for centuries after. The Christian tribe of al-Jurajima that lived near Antioch sided with the Muslim armies against Byzantine forces and so did the Coptic Christians of Egypt who preferred to be ruled by Muslims than their coreligionists. This attitude of the Muslim rulers towards their subjects was unparalleled in history. The Muslim attitude of war was not a holy war even though the attitude of those who were fighting was holy in mind i.e. fighting against oppression, but the wars itself were never intolerant religious conflicts, as still portrayed in the Western minds, for had they been like Crusades, Muslim armies would not have been tolerant towards their non-Muslim subjects. This is because intolerance is something which clearly contradicts the teachings of Quran which the early Muslims were very strong in following.
Thirdly when doing a comparison, Muslim wars against Byzantine and the Crusades against Muslims are 2 completely opposite things. The crusades were specifically waged with the concept that Muslims and Islam was a scourge and it needs to be eliminated. This propaganda, of which the primary source was the Pope himself, was proven by the treatment of the Muslims by their European conquerors. Mass murders and rape of Muslims was their attitude, they considered these acts justified according to the interpretations taught by their church. On the other hand Muslims were guided by principles to respect other people’s faiths and honor their lives and properties as long they are not rebellious. A simple comparison of the Muslims when they entered Jerusalem, with that of Crusaders clarifies this for us. When Jerusalem submitted to the Prophet's 2nd successor and Caliph, Umar ibn al-Khattab (r.a) he made the following agreement with the Christian Patriarch Sophronius of the city:
"In the name of God, the Merciful, the Compassionate. This is the assurance of safety which the servant of God, ʿUmar, the Commander of the Faithful, has given to the people of Jerusalem. He has given them an assurance of safety for themselves, for their property, their churches, their crosses, the sick and healthy of the city and for all the rituals which belong to their religion. Their churches will not be inhabited by Muslims and will not be destroyed. Neither they, nor the land on which they stand, nor their cross, nor their property will be damaged. They will not be forcibly converted. And [as per the Christians’ request] Jews will not live in the same areas as them."
The following are short accounts of how the Crusading Kings of Europe when entered the same holy city slaughtered its inhabitants. The following chroniclers of the First crusade recorded their accounts of the incidents as mentioned in "The Siege and Capture of Jerusalem: Collected Accounts". According to the Gesta Francorum, speaking only of the Temple Mount area, "...[our men] were killing and slaying even to the Temple of Solomon, where the slaughter was so great that our men waded in blood up to their ankles..." According to Raymond of Aguilers, also writing solely of the Temple Mount area, "in the Temple and porch of Solomon men rode in blood up to their knees and bridle reins." Writing about the Temple Mount area alone Fulcher of Chartres, who was not an eyewitness to the Jerusalem siege because he had stayed with Baldwin in Edessa at the time, says: "In this temple 10,000 were killed. Indeed, if you had been there you would have seen our feet coloured to our ankles with the blood of the slain. But what more shall I relate? None of them were left alive; neither women nor children were spared."
Much of the reason why Muslims were welcomed by the Christian residents of the lands they conquered were because their Byzantine rulers belonged to the Orthodox Church which displayed intolerance towards Christians of other thoughts and persecuted them. The Muslims gave them the opportunity to practice their Christian faith as they wished without restrictions. T. W. Arnold writes further how the Coptic Christians of Egypt welcomed the Muslim army under Amr ibn Al Aas (r.a), a companion of Prophet Muhammad ﷺ:
“The Jacobites, who formed the majority of the Christian population, had been very roughly handled by the Orthodox adherents of the court and subjected to indignities that have not been forgotten by their children even to the present day. Some were tortured and then thrown into the sea; many followed their Patriarch into exile to escape from the hands of their persecutors, while a large number disguised their real opinions under a pretended acceptance of the Council of Chalcedon. To these Copts, as the Jacobite Christians of Egypt are called, the Muhammadan conquest brought a freedom of religious life such as they had not enjoyed for a century. On payment of the tribute, 'Amr left them in undisturbed possession of their churches and guaranteed to them autonomy in all ecclesiastical matters, thus delivering them from the continual interference that had been so grievous a burden under the previous rule; he laid his hands on none of the property of the churches and committed no act of spoliation or pillage.”
History bears witness to the fact that Muslim expansion in the earlier years of Islam were not due to prejudice, hate, racism based on a religious pretext. Yes Muslims did attack their opponents and defeated them and build an empire on their lands but provided justice which the people of that land were deprived of. These people were yearning for someone to come save them from the persecution they faced at the hands of the authorities ruling over them. Therefore even though the Islamic Conquests of 7th Century CE happened first, but the factors guiding their conquests were not intolerance and hatred like that of Crusaders.
 al-Mubarakpuri, Safi-ur-Rahman. 1996. Al-Raheeq Al-Makhtum (The Sealed Nectar). Dar-us-Salam Publications.
 THE PREACHING OF ISLAM A History of the Propagation of the Muslim Faith - Pg 47 Chapter III - The Spread of Islam Among the Christian Nations of Western Asia
 THE PREACHING OF ISLAM A History of the Propagation of the Muslim Faith - Pg 48 Chapter III - The Spread of Islam Among the Christian Nations of Western Asia
 Recorded in Tarikh Al Tabari, - https://www.islam21c.com/islamic-thought/the-treaty-of-umar/#_ftn2 - also quoted in THE PREACHING OF ISLAM A History of the Propagation of the Muslim Faith - pg 49 Chapter II.
 Medieval Sourcebook: The Siege and Capture of Jerusalem: Collected Accounts - History Department of Fordham University, New York https://sourcebooks.fordham.edu/source/cde-jlem.asp#fulcher1
 THE PREACHING OF ISLAM A History of the Propagation of the Muslim Faith - pg 83 - Chapter IV - The Spread Of Islam Among The Christian Nations Of Africa