THE POSITION OF ESP IN ELT

To understand the position of ESP in ELT, you can look at the ESP tree below. 

(Sources:

1       Hutchinson, Tom and Waters, Alan. 1987. English for specific purposes: A learning-centred approach. Cambridge: Cambridge University Press p. 17)

If you look closely at the tree, you know that ELT is divided into EMT (English as a mother tongue), EFL (English as a foreign language) and ESL (English as a second language). ESP it self is one of the branches of ELT. So, in ELT you have both GE and ESP. GE is the teaching of English at school while ESP is the teaching of English for more specific purposes.