I am of the thought that it is very much a crusade, because there is no reason to believe the actual crusades were anything beyond riling up the peasants for the benefit of the rich.
Let's suppose you've managed, as a family, to hack and slash your way to the top of the nobility. Grandfather was a friend of the guy who became king, father inherited lands and got them productive, and now five brothers have all survived. The eldest gets the land. The next four have learned to ride horses, swing swords, and wear armor. One of them decides that the Church isn't so bad, and thus effectively goes into politics. There are still 3 armed badasses who won't be getting the power and wealth they are used to... unless they go and take it from someone else.
Their brothers in the Church have an idea: maybe you can go be violent somewhere else?