Non-social. Anything that you don't 'commonly' dance at normal everyday functions.
So, ballet for sure, tap as well. Jazz I'm not too sure about where that comes.
Terminology.
Ballroom, used in England to mean both the ten international style dances or only the five standard dances (determine by context or ask).
Standard, International Style ballroom comprising Waltz (sometimes referred to as modern waltz or English waltz), Viennese waltz, slow foxtrot, tango and (my favourite) quickstep.
Smooth is the American Style (sometimes also known as Social Style)comprising of (help me out here) modern waltz, foxtrot, viennese and tango.
Social style, aka American Style, but can also refer to dancing in a social setting. Both American Style and Intenational style can be danced socially or competitively (mainly International in Canada and the rest of the world except for the states).
Latin - International Style referring to rumba, cha-cha, samba, jive and paso doble (a dance I would consider to be a non-social dance as it is not frequently danced even in the social ballroom world, perhaps one a night but usually only by request).
Rhythm - American Style, comprising rumba, cha-cha, bolero, swing, mambo.
Hope I have this right.
Hope it helps.
D-spot.