Traditionally, AGI means being capable of learning everything (not necessarily at once) that can be learned by the same AI agent. It differs from the commercially meaningful definition in that a standard specific-purpose-built AI can still do most tasks if you give it enough specific purposes, but it will be just as incapable of human intelligence as ever.

No - the term "AGI" was really coined to distinguish general intelligence from narrow intelligence(s). There's an obscure earlier usage, but it basically became mainstream as the title of a book edited by Ben Gortzel who had in turn got it from Shane Legg.

Shane Legg would a few years later go on to co-found DeepMind, with creating AGI as their declared mission. Legg's personal definition of AGI is not just generalist AI, but specifically human-level generalist.