(T)ESOL: (Teaching) English to Speakers of Other Languages
The expression which is used to cover all forms of English teaching to non-English speakers; sometimes also used instead of EAL or ESL – see below.
ELT: English Language Teaching - a general, inclusive term used in the profession.
EAL: English as an Additional Language
English taught to non-English speakers who live in the UK and who need English for study or other purposes, in Primary, Secondary and Tertiary Education. EAL was formerly referred to as ESL (English as a Second Language) or E2L.
(T)EFL: (Teaching) English as a Foreign Language
English taught to learners, both overseas and in the UK, who may have no intention of living in an English-speaking country.
Note: There are many similar expressions which relate to aspects of ELT which are not of immediate concern here. The most common are EIL (English as an International Language), LFE (Lingua Franca English), ESP (English for Specific Purposes), EAP (English for Academic Purposes), EYL (English for Young Learners), etc.