Finally found where they hide all the information on English language teaching in Wikipedia. Apparently, the acronyms I already know (ESL, TESOL) are not enough and we need more acronyms to amaze and bewilder our colleagues with. There's a long list at the bottom of the page.
English as an Additional Language (EAL), I guess, is not the same as ENAL (English as Not an Additional Language). Maybe we're all EEL's (English as an Expat Language) because we speak slower and use less vocab.
Many relevant entries are filed more reasonably under language acquisition, but there's some obvious advertising that they don't let into this category like the Pimsleur language learning system or accelerated language learning, see discussion, but to be fair to Pimsleur, Nation cites Pimsleur's "Forgetting Curve" in his classic book on teaching vocabulary (See review and also see Waring's Basic Principles and Practice in Vocabulary Instruction).