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?