

https://en.wikipedia.org/wiki/Developed_country
Developed vs developing vs undeveloped are pretty well defined. They are relative terms. So sure you could in theory move from developed to developing, that kind of thing happens very rarely though.
I do agree that “developing” implies progression towards developed, so a more accurate term would be something like “partially developed” but its clunkier. Overall though I think they are far more accurate terms than the alternatives.
Well, I wouldn’t say that “developed” implies countries aren’t trying to improve themselves further, any more than “rich” people aren’t trying to get richer. You can call it whatever you want but at the end of the day you need to have some terms to describe poor countries where people die of treatable diseases because they lack infrastructure and money, and countries that don’t (as an example). Global South is just a euphemism for the same but a lot less intuitive and accurate.
There isnt a developing country on the planet that isn’t trying to be considered developed.
And I dont think this is a particulary American term. Third-world, sure.