I know our school doesn't consider us a Greek sorority - a fact that has several of the Greek groups (even the ones I have several friends in) treating us rudely or shunning us on campus. Kinda sucks - I would like to see more unity between organizations - but I love my sisters, and as much as I love girls in some of the other groups, I wouldn't be in a different sorority to save my life!
I think the term service Greek is very appropriate.