I've always thought of the 'first world' as countries with modern technology and science, proper education, viable economies, and freedom from other social issues which allows individuals to enjoy a higher standard of living. In short the sort of country that would have general similar standards of living as the US or England. By my personal definition, which seems to be the way most use the term within the US, places like Sweden, Japan, and pretty much all of the EU would count as a first world countries.
I've meanwhile thought of third world nations as place with severe poverty, poor education or technology, and often other social issues preventing them from modernizing like war, corruption, or famine.
However, I looked it up today and found out that Wikipedia disagrees with my personal definition: https://en.wikipedia.org/wiki/First_World. Essentially a first world nation is officially defined as "everyone the US liked during the cold war". Japan, meanwhile, is defined as a third world nation; which it definitely would not be under the definition I always used.
Is there a better term that actually defines what I thought of as a first or third world country? Preferable as non-derogatory as possible in the case of referring to a place as third-world? I know any term for a place with poverty will inevitably have a negative connotation, but if I want to discuss, for instance, the mortality rates of a disease in 'first world' vs 'third world' conditions (as I use to interpret them) to analyze the effectiveness of modern sanitation and medicine...what is a good clinical term to define such areas?
Related, Do other places outside the US use the terms first world and third world? if so how do they generally use them?