Let's see here
Bourgeoisie:
includes grande (big) and moyenne (medium) bourgeoisie, but essentially they are medium (regional/national) and large (global) capitalists, that mainly rely on industrial profit, if not landed rend, and financial interest, based around growing industrial and financial production
Though I consider bourgeoisie in its western context, to specifically refer to the first modern form in Europe, birthed from the Medieval period
Bourg-eois --> Bourg derives from the medieval German term for "city", as they derived from the growing cities of their era
Petty-bourgeoisie:
a small business owner (only a handful of businesses directly owned by them)
Proletariat:
wage/salaried laborers who depend heavily on their wage/salary, lest a few days/weeks leave em destitute and homeless
They are historically converted from the destruction of peasants, yeomanry, guild craftsmen, apprentices and mentors, during the progressive bourgeois revolution against feudalism.
Originally, in Rome, such term was derived from those citizens who made offspring to serve the Roman slave mode of production
Lumpenproletariat
despite its name, it is a similarly newly-created class of capitalism, more destitute and ruined than the proletariat, defined by a lack of official joblessness and stability, which include people from the simply unemployed and unhoused to criminals, strike-breakers, prostitutes, and gangsters
They are a wild card that can ally with either bourgeois or proletariat forces
Lumpen (rabble) + proletariat
Depends, there's many in history that can fit the bill (eg. feudal lords (crop rent), industrial capitalists (factory profit), slaveowners (goods and free labor profit), and aristocracy of finance and land (money interest and land rent) )
Professional managerial class, or compradors for the main dominant capitalist group (eg. the West) / hegemonic capitalist group
Proletariat and lumpenprole?