The reason some people treat these as equivalent is that AI algorithm research is one of the things a well-educated adult human can do, so an AGI who commits to that task should be able to improve itself, and if it makes a substantial improvement, then it would become or be replaced by an ASI.
To some people this is self-evident so the terms are equivalent, but it does require some extra assumptions: that the AI would spend time developing AI, that human intelligence isn't already the maximum reachable limit, and that the AGI really is an AGI capable of novel research beyond parroting from its training set.
I think those assumptions are pretty easy to grant, but to some people they're obviously true and to others they're obviously false. So depending on your views on those, AGI and ASI will or will not mean the same thing.
To some people this is self-evident so the terms are equivalent, but it does require some extra assumptions: that the AI would spend time developing AI, that human intelligence isn't already the maximum reachable limit, and that the AGI really is an AGI capable of novel research beyond parroting from its training set.
I think those assumptions are pretty easy to grant, but to some people they're obviously true and to others they're obviously false. So depending on your views on those, AGI and ASI will or will not mean the same thing.