Bourgeoisie, from what I've searched, relates to the term "burgh" and it seems to translate into post-medieval prospering city-dwellers, so to speak, in its historical context, perhaps the forerunner and early form of capitalists; the break from feudalism, with its feudal lords, monarchies, and guilds
Capitalists, as such, are its own distinguished broad class that are growing via exploiting of wage labor for their surplus value, now in our present times, free from the fetters of feudalism, and ripe to compete and expropriate
Am I correct on these two parts, or is there something I'm missing?
Honestly it has always been my impression that there is no real difference between either of these terms. "Bourgeois" comes from "burgh", yes, in Norwegian "the bourgeoisie" is called borgerskapet from the same root — but "etymology" is not literally "the study of the true meaning".
