Bush is a dedicated Protestant, not Catholic.
And was Blair was a secret Catholic at the time of supporting the invasions, even the Catholic Church spoke out against these wars, particularly the Iraq invasion.
The arabs did not need a name for the Crusades, because they were just a small part of the overall jihads waged by generations of Muslims against the West.
Earlier Jihads were to expand the lands under Islam. During the Crusades, the purpose of the jihads changed to defending the lands of Islam.