I don't have formal education in the field, but I hang out, in CSTM, with many people who do. Nowadays they tend to call themselves "ethnomusicologists"; "folklorist" seems to have a vaguely old-fashioned feel. (Edith Fowke used to insist, rather defiantly, that she was a folklorist, not an ethnomusicologist.) I think ethnomusicologists will deal with non-traditional as well as traditional music, as long as it's culture-based. Also, folklorists will deal with non-music material, such as folk tales, customs, adages, etc., as long as it's traditional.

A "collector", as someone said above, is someone who learns music directly from informants within a tradition. Just to further complicate things, a "compiler" puts together collections of material that other collectors have collected.