Yes, they mean approximately the same: someone whose primary language is not English is now learning English.
ESL stands for English as a Second Language.
ESOL stands for English to Speakers of Other Languages.
ELL stands for English Language Learners.
EFL stands for English as a Foreign Language.
ESP stands for English for Special Purposes.
TESL stands for Teaching English as a Second Language.
More and more I am seeing ELL as the current politically correct term in the US. Just a few years ago it was ESL. But I hear that in the UK and Ireland, ESOL is the preferred term.