This Wikipedia article can help those out there lost in what I refer to as TOEFL Salad, meaning the many and varied acronyms for learning and teaching the English language. That includes ESL, EFL, TESL, TEFL, TESOL, ESOL, ESD, EAP, EOL... you get the point.
Of course, the article also does a lot more than that, delving into English learning and instruction in English- and non-English-speaking countries, differences between spoken and written English, systems of simplified English, the many varities of English and more.
ESL (English as a second language), ESOL (English for speakers of other languages), and EFL (English as a foreign language) all refer to the use or study of English by speakers with a different native language. The precise usage, including the different use of the terms ESL and ESOL in different countries, is described below. These terms are most commonly used in relation to teaching and learning English, but they may also be used in relation to demographic information.
ELT (English language teaching) is a widely-used teacher-centred term, as in the English language teaching divisions of large publishing houses, ELT training, etc. The abbreviations TESL (teaching English as a second language), TESOL (teaching English for speakers of other languages) and TEFL (teaching English as a foreign language) are all also used.
Other terms used in this field include EAL (English as an additional language), ESD (English as a second dialect), EIL (English as an international language), ELF (English as a lingua franca), ESP (English for special purposes, or English for specific purposes), EAP (English for academic purposes). Some terms that refer to those who are learning English are ELL (English language learner) and LEP (limited English proficiency).
Read the Wikipedia article on English Language Learning and Teaching.