Academic Vocabulary is defined as words that are traditionally used in academic dialogue and text. Specifically, it refers to words that are not necessarily common or frequently encountered in informal conversation.
Domain-specific words are words used when talking about one thing. for example. if you were talking about a microscope, the conversation will consists with words that are only related to a microscope(like the name of the parts ) so those would be domain-specific words. Hope that makes sense, sorry! XD