I'm sure there are others who can give a much better legal definition of "incorporation," but it is a legal term.
Small businesses are not "incorporated". We are a small business and thus are not.
I have another business. It's called The Everlasting Companies, Inc. It is not a legally registered corporation, but by definition it is one. It consists of Everlasting Films, Everlasting Word Publications, and Everlasting Dreams Real Estate. I'm certain there are a thousand things wrong with all that, so I hope no one will clog the thread by pointing all them out.
But there's the quick-and-dirty difference.
My understanding is that an unincorporated business may be registered or otherwise. If it's the former, then it's technically not a business: rather the one operating it is a business. That means any profits and losses are usually included in one's personal tax returns.
If it's registered, then it's still an unincorporated business but has advantages similar to that of an incorporated one, such as ownership of the business name, the ability to sell it to a third party, ease of incorporation, etc. But like the latter, it may have similar requirements, such as getting business licenses, various permits, etc.
The point is that all legally registered businesses require legal systems (hence, "legally registered") and the purposes are practical. Since these businesses are part of capitalist systems, then the latter require legal systems for obvious reasons. The same applies for even non-registered businesses, which still need fiat currencies, legalization of ownership of the means of production, etc. All that is part of government regulation, which in turn is part of socialism.
The counter-claim raised in this thread is that capitalism is the opposite of socialism, which makes no sense at all as (a) capitalism employs regulations for reasons given above and (b) socialism isn't against capitalism but private ownership of the means of production.
Both "wokes" and their critics appear to be unaware of these points.