What is TESOL?
TESOL stands for Teaching English to Speakers of Other Languages and encompasses what used to be called TEFL (Teaching English as a Foreign Language) and TESL (Teaching English as a Second Language).
What is Applied linguistics:
is an umbrella term that covers a wide set of numerous areas of study connected by the focus on the language that is actually used. The emphasis in applied linguistics is on language users and the ways in which they use languages, contrary to theoretical linguistics which studies the language in the abstract not referring it to any particular context, or language, like Chomskyan generative grammar for example.