I notice that none of those categories are "figure" skaters.
Seems to me that there are two different categories involved here: the level of involvement (recreational, test, competitive, etc.) and the subdiscipline (freestyle, dance, synchro, figures, etc.). Both have fuzziness… for example, right now I'm working on basic skills, don't take privates normally, but am about to work with a coach for an ISI Alpha level competition. But I wouldn't call myself a competitive recreational skater, since I'm not even onto the real test track yet.
I think I'll just keep it simple. I skate.