It can be very confusing. Here are a few of those acronyms explained:
EFL: English as a Foreign Language – in countries where English is not the first language. The industry name
TEFL: Teaching English as a Foreign language – Teaching it
ELT: English Language Teaching – the term that covers EFL and ESL
ESL: English as a Second Language – to people who live permanently in an English speaking country, but whose first language is not English (often immigrants and refugees). The closely related but different industry
(T)ESOL: (Teaching) English as a Second or Other Language – pretty much the same, except it recognises that for many people English is their third or fourth language
Trinity Cert: Another body that provides a pre-service 4-week courses
CELTA is by far the best known and most widely taken initial 'TESOL/TEFL' qualification of its kind in the world, taken by over 10 000 people every year. CELTA is accepted throughout the world by organisations, which employ English Language teachers. The Cambridge CELTA has been accredited by the Qualifications and Curriculum Authority (QCA) at level 4 on the U.K. National Qualifications Framework. Cambridge ESOL also works with international ELT organisations to ensure the acceptance of CELTA globally.