Is there a difference between saying "greatest album of all time" and "favorite album of all time?" To me, my greatest album IS my favorite, but for some reason people respond differently when I switch them.

Saying that there is a difference between the two implies that there is a definitive "greatest albums" list, when there really isn't. Objectivity doesn't exist in music, so we shouldn't have to be clarifying when it is our opinion or not. Everything is our opinion.