Your confusion is fair, considering that, up until two weeks ago, Google Meet was actually called Google Hangouts Meet. And yes, it is a completely and entirely different service.
Hangouts is still the legacy chat program that featured some video and voice call capabilities. Meet is their Zoom competitor, built for GSuite users, and is under active development and is a very solid product with very strong video/voice performance, up to 250 attendees, dial-in numbers, live transcriptions, recordings, screen sharing, etc.
They rebranded it as Google Meet literally two weeks ago. They are killing Hangouts Classic. They have... also spun up Google Chat (formerly Hangouts Chat) which is... a pseudo-competitor to Slack, and an evolution of Hangouts, but only for GSuite users, with the intent of killing Hangouts Classic (the evolution of GTalk) early next year.
Meet is far more advanced and better supported that the legacy Hangout for a conferencing tool. It is far better, and we really prefer it. (Though, because it also bears mentioning, Google is ALSO working on Duo, which is their CONSUMER video chat program, which has some neat features, like AI audio gap-filling and super-low-bandwidth AV1 codec benefits, which I hope make the jump over to Meet soon...)