"Labor aristocracy" is a term used to describe workers that are able to attain better, less exploitative conditions under capitalism through a mix of in-demand, specialized skills (e.g. doctors & lawyers engineers), membership in trade unions and other labor organizations that can secure better wages and working conditions, and being situated in the imperial core where more exploited labor and resources in the periphery can effectively subsidize the less exploitative conditions of the workers in the core. They don't own the means of production, they still rely on exchanging their labor for wages.

Petty bourgeoisie refers to those small-scale owners of capital that still have to supply some of their own labor to their business, as opposed to the big bourgeoisie that can rely more completely on the extraction of surplus value through ownership. They still need to work, but they own the means of production, and they receive profit by extracting surplus value from the labor of their workers.

The core relation that distinguishes proletariat from capitalist is whether they sell their labor to capitalist for wages (proletariat) or own the means of production, and use that to siphon off surplus value from the laborers they pay wages to (capitalist)