USA-Israel relations explained

It's a signifier for a politico-economic concept, so yes. Third world is a similar signifier that also doesn't really align with its original nor intuitive meanings. Semiotics is weird like that.

Either one can be used to signify countries from which resources and labor are extracted by the Global North or something along those lines. Do they find themselves richer or poorer due to global trade?

For example, Australia, in this context, wouldn't be considered global south despite being in the southern hemisphere. Unless it was harshly colonized and became a resource trough for the USA and Europe, then its politico-economic position would change even though it obviously didn't change geographically.

Wait till you learn about the American South.