Just to note, that's explicitly what "third world" was intended to express. Alfred Sauvy coined the term by analogy with pre-revolutionary France, with the Third World countries being those outside either Western powers or the Eastern Bloc, all those countries that were and are sites of exploitation. Maoist Three-Worlds-Theory was a historically contingent recapitulation/reworking of that with the US and Soviet Union as the first world, the Second World being the other countries of the Global North and "developed" Communist bloc and the Third World being colonised and post-colonial unaligned countries that were ostensibly sites of exploitation for both superpowers. It's only the Western "popular" understanding that depoliticizes the concept.

Also "Previously Colonized Countries"... eh. That implies that colonialism and imperialism is a thing of the past instead of absolutely present and current, even if the contingent "performance" of colonialism is different...