ELT stands for English Language Teaching - a general term that includes EFL and ESL.
Other related abbreviations:
EFL stands for English as a Foreign Language, i.e. teaching English in a country where English is not generally spoken.
ESL stands for English as a Second Language, i.e. teaching English in a country where English is generally spoken.
ESOL stands for English for Speakers of Other Languages. This is a general term that includes EFL and ESL.
ESP stands for English for Special Purposes. This can include EPP, but also special cases such as Survival English for newly-arrived immigrants.
英语教学方法简介
功能交际法与语法翻译法
The Communicative Approach功能交际法: A method of teaching that focuses on helping students communicate meaningfully in the target language. With this approach there is a tendency to place more emphasis on speaking and listening tasks.
Grammar / Translation method语法翻译法: An old-fashioned teaching technique that involves rote learning of verbs and vocabulary, together with translation of sentences from L1 to L2 and vice versa. Just because it's old fashioned doesn't mean that it's wrong! In fact, translation (as a way of comparing L1 and L2) is back in favor as an ELT tool.