What is a similarity between the crusades and the inquisition?

Both the crusades and the Inquisition believed that violent measures (such as killing, invading, torturing) were justified if they served to spread the one religion perceived as true by the ones engaging in it. In both cases this religion was Christianity, and specifically the Roman Catholic Church and in both cases the popes endorsed and encouraged, or even initiated the events. In both cases a big number of people died, but the deaths of non-Catholics were not considered a negative outcome, but a part of combating heresy or other religions.