- "third world" should include Switzerland and Austria, as they were neutral during the cold war
- "developing countries" should not include places in major wars or civil wars (such as for example not Yemen), as they're clearly not developing, but rather deteriorating.
- as you point out, "global south" should include the wealthy Australia.
It also expands into other examples of hypocrisy, such as the term "African-American", which is just an euphemism for black Americans (which itself suggest that being black is bad somehow), but due to its clumsiness also includes lots of non-black people, such as Tunesian-Americans (no black people there).
Yes, that's it. You said it better than I did.
I had no idea it was related to the USSR at all and had just assumed third world strictly meant a poor nation