EFL – English as a Foreign Language – is the name given to the English taught in commercial language schools. Students are typically young people who have come to an English-speaking country for a period which may range from a couple of weeks to a full year, with the main aim of improving their English. The meaning of the term is that teaching English as a foreign language requires a whole range of skills and approaches which are not used in teaching (say) children their own language. The term often also covers teaching English to specialists or academics, and to lessons that people take in private language schools in their own country.
ESL or ESOL – English as a Second (or other) Language – is more aimed at people who have come to an English-speaking country to live, by choice or (as in the case of refugees, for example) from necessity. ESL is often taught in colleges, Adult Education centres or other government-funded organisations. The aim is primarily to prepare students for life in the host country, so typically lessons contain much more "survival English" (things like filling in forms and going for interviews) and information about the host country than EFL classes do. In practice, however, the two often overlap.