I think the alphabet soup is that TESOL = both TEFL + TESL.

There's an organization called TESOL International, http://www.tesol.org . They set standards for TESOL courses, but they don't conduct audits or certify that any particular course really meets them.

I was looking at a completely-online TESOL course from Arizona State University, because a student of mine is interested in getting a TESOL certificate. (I'm only an informal volunteer teacher, at our local public library, so I don't have any certification myself). They phrased it this way: "Arizona State University has created a TESOL Certificate Program available completely online... [it] follows TESOL''s high standards for a TESOL Certificate Program (for reference, see TESOL International Association’s Standards for Short-Term TEFL/TESL)."

It seems to me that whatever program you look at should say, somewhere, what standards it claims to meet (even if you are trusting them to really meet them). 

So, for example, if someone said "ASU? Never heard of them," a student could say "It's a 150-hour course that follows the TESOL International Standards for Short Term TEFL/TESL." Then at least they'd know what the course is supposed to cover.

There are two broad categories:  Teaching English as a Foreign Language (for teaching general and academic English for school age learners in non-English-speaking countries) and Teaching English as a Second or Other Language (general English for adults and school age children in English-speaking countries).

As a generalization, an English teacher in an Asian country will teach grammar and academic vocabulary and give students lots of practice taking English exams.

An English teacher to immigrants (my situation) will teach core vocabulary and give students lots of listening and speaking practice and role-playing practice for everyday situations such making a doctor's appointment.