[thaumasiotes]

> Imagine mathematicians calling commutative groups abelian? How do you remember if xy=yx there?

Actually, even if you ignore jerf's response, this is different in an important way from the "Type I" / "Type II" terminology.

Group in which the group operation is commutative: "Abelian group".

Group with no guarantees except the group axioms: "group".

The special one is marked and the non-special one is unmarked. In contrast, the designations "Type I" and "Type II" are parallel; it's not at all obvious which one is the default and which one deviates from the default.