A popup is a larger object, often a full window, that covers large parts of other elements or sometimes the entire screen. They are sometimes modal.
A toast is a smaller element, appearing (often by sliding into view upwards, hence the cutesy name) in or above a specific notification area of the application or the overall OS. These are much smaller, seldom modal and often convey useful notifications or warnings, unlike popups (especially modal ones) that are often either useless or actively, deliberately, in the way.
While it is correct to call then both popups if you wish, "toasts" are generally considered a specific subset.
I pasted this into Google to see what you were referencing, and was met with this full-screen, front page, all-important "AI Overview" (that of course takes precedence over actual search results)
> You're very welcome! If you have any questions about the Sirius Cybernetics Corporation's products, their marketing strategies, or need assistance with anything else, feel free to ask.
Full circle.
Every time I see a new CoPilot button, or a toast nagging me because I've not clicked any of them and they think I really should want to, a phrase crosses my mind…
“Thank you the marketing division of the Sirius Cybernetics Corporation”