E.S.L.: English as a second language, meaning students will be speaking English outside of the classroom. Think of exchange students as the most obvious examples.
E.F.L.: English as a foreign language, meaning students only speak English in the classroom, and rarely outside of it. Think of non-English major Korean students like the ones I teach here in lurvely Daegu.
E.I.L.: English as an international language, a newer acronym which implies English is going to be spoken in almost all situations where a second language is required.
E.L.F.: English as lingua franca, which is similar to E.I.L. but implies a situation where two people who need to communicate are forced to use English. Sort of the pessimistic / somewhat less colonial version of E.I.L.
And this, friends, is how I spent my Saturday. I do feel like I’m making progress though, and I’ve read some pretty interesting, albeit dry, papers on this stuff.