One extra point for the OP: many Star Alliance airlines have individual relationships with airlines that aren't Star Alliance members. Bangkok Airways has codeshares with two Star Alliance carriers - Thai and EVA - but they have relationships with a bunch of other airlines that are members of SkyTeam or OneWorld or are unaffiliated. You only get bennies with Star Alliance carriers, and more frequently on the mainline carrier and not affiliates. Thus, if you were flying Thai, you could use their lounges as a paid United Club member. But, if you were on their subsiderary, Thai Smile, you would not, as the affiliate is considered a separate carrier and is not affiliated with Star Alliance.

It's confusing for US and Canadian flyers. Yeah, United has had things like Ted and United Shuttle before, the "airline within an airline" setup, but as far as FF programs, there was no difference between a Ted and United flight. With the international carriers, that is not always the case.