AGI is the term invented because arguments about what AI meant had gotten annoying. Originally there was no distinction and people thought "AI" would mean human level intelligence. Chess and conversations and robotics and math all in one package. Then games and classification and some robotics got solved and called AI, but that didn't solve math or conversation or online learning or a host of other things, so AGI was coined to refer to most of the whole package, virtually all the capabilities you'd need to replace humans intellectually. Now we're quibbling about whether AGI includes robotics or full real-world physical agents or something less.

The consensus now seems to be that once you've got human-level intelligence and planning and executive function then you get recursive self-improvement that can eventually autonomously solve the robotics and world-modeling and other portions of human-equivalence.