* ferromagnetic - attracted to one pole of a magnet but not the other (in a given orientation), this is what everybody thinks of when they think of "magnets"

* paramagnetic - attracted to both poles, i.e. stuff that sticks to magnets

* diamagnetic - repelled by both poles, except in superconductors, this effect is very weak compared to the forces experienced involving ferro-ferro or fero-paramagnetic materials.

There isn't another category, everything fits in to one of those buckets.

Saying

>Just so everyone is on the same page, static passive diamagnetic levitation is possible with materials like pyrolytic graphite.

is a bit deceptive, as what people know as "magnetic" materials are ferromagnetic.