The West I typically say in reference to philosophy and ideology. Specifically ideas surrounding a linear, progressive view of history and morality. Some marxists fit into this quite easily.

The Global North vs South is useful because it’s a less anachronistic way of talking about “first world” and “third world” by removing the context of the Cold War. Most rich countries are in the North with minor exceptions.

Then there is world systems theory which uses core, semi-periphary, and periphery. This is usually more specificly about capital. Where is the capital? Where isn’t it? Sometimes financial capital is prioritized and sometimes it is productive capacity. Technically, this does not entirely apply to nation states, but can also apply for certain sectors. If you have concentrated capital in one sector (like agriculture) you might be considered core for that sector but not in a sector you have no capital for (idk like satellite tech or something) so you are peripheral in that sector. This is especially true in semi peripheral countries like the BRICS countries. There is also the (oversimplified) implication that core countries exploit and peripherals are exploited but semi-periphary nations very basically do both and are sort of caught up in the greater global system in one way or another so as to develop sovereignty. What is important however, is the interrelationships of nations.

Many of these distinctions are exhausting because as you point out they usually are talking about the same thing. So what is that? Well I’d say it is the continuity of colonialism as it is manifested in the present “globalized” world. It stands on certain philosophies and is visible in geography. The terminology is usually more important to nerds but I think at the end of the day it describes how some parts of the world enforce domination on to other parts to maintain class society which is fueled by imperialism.