Crusades are the logical evolution of the christianised institution of milites through the XIth century and the reinforcement of clerical institutional power. If violence against Christians from a class whom whole legitimacy was based on warfare was frowned upon, the logical outcome for milites, in order to be religiously legitimized, was to use this violence to serve Christians.
I would really really disagree with what Danth proposed as objective of Crusades : protecting pilgrims was already a thing at least one century before (as well armed pilgrimages), Mediterranean basin already was under latin dominance at this point (that's actually one feature that allowed Crusades to be a thing : without italian presence in ME already established, there would be no reinforcement or ravitail possible in first place), and "uniting Europe" is at best a romanticist vision (would it be only because Europe as a concept didn't existed).
Legitimisation of violence and more generally of a military-based social class (less nobility as a whole strictly speaking than milites, aka warring nobility) that is in the direct continuation of Truce of God and XIth councils (it did help that Urban II was issued from this nobility, and most able to speak to them as they could agree with) played the most important part there.
The consequences : conquest, loot and else was more issued from warring than a real planned objective (The constant infighting and hesitation of the nobles supposedly leading the expedition point that).
In this regard, Jihad (I won't go into subtilities about "greater/inner jihad" : for centuries, the best and more widespread expression of jihad was military conquest and expansion of Dar al Islam.) is quite similar : you have there the legitimization of razzias and conquests already practiced by pre-Islamic Arabic society but at the condition it's not made against Muslims but against other regions.
The social configuration is of course quite different, but we have the same essential reasoning.
There's some differences, but more temporal than essential as well.
Crusades were the answer against Islamic expansion. It's made clear by contemporary texts that loss of Spain and Jerusalem were put in the same bag with different recalls of earlier expeditions.
Interestingly, the Crusades provoked eventually among Muslims a revival of Jihad as military expedition, especially by Saladin : on this regard again, we have a religious expedition or ideological base lead against what was percieved against an aggression.
The parallel is really close there : it wasn't before Arabo-Muslim world really percieved the religious/social nature of Crusades that it was able to provide an answer (already existing in its traditions) at the same measure; as it wasn't before western Christianity really percieved the holistic religious/social nature of Arabo-Islamic world that it was able to think an answer.
I would go with Jihad being both the precedent Islamic version of Crusades, and its answer. Differences exists, but similarities are far more present.