EFL- students are not living in an English-speaking country.
ESL/ESOL- students are living in (or planning to) an English-speaking country. This term is the same as
ESL, but
ESL is used in the USA and ESOL is more common in the UK and Australia.
Training in
ESL does not mean that you are incapable of teaching in an EFL environment, vice versa. However, like ICAL_Pete, I think that contemplating doing an MA is a bit premature here and you would be better off sorting out the language basics before atempting post-grad studies.