Either term is acceptable, but I believe Foreign Object Damage is much more widely used, especially in the military aviation context. Here's one link out of many. During my flying days in the Navy we always referred to it that way. Even when we did our end to end carrier flight deck FOD walkdowns to pick-up stray bolts or safety wire, we didn't redefine the acronym. I guess it was just a colloquialism that extended to mean both the item and damage.