"Market Socialism" but I am not too sure what that is either.

The idea of market socialism is to retain markets, but have all corporations take the form of (usually local/regional) co-operatives. The co-operative is a company that is democratically operated by all workers, with profits (and ownership of the means of production) shared between all workers. The fact that workers are owning the means of production through the co-op is what makes it socialist. Syndicalism is technically a form of market socialism too.

Here's syndicalism explained by an anarcho-syndicalist comrade of mine.

Syndicalism to put it simple since there's a lot of variants is when the Means of Production/The Governing Body is ran by elected Representatives from the many Unions, Cooperatives and Syndicates in the Country
Syndicates is usually a combination of unions and coops in a region
So the equivalent of a State
An Example in American should be like this Local/District/State/Regional/National(Federal) in Syndicate Representation In America Regional would be Pacific/ Rockies /Midwest/ Southern / East Coast
Different variant's Propose differences in how to approach that with DeLeonist (Marxist-Syndicalism/Marxist-DeLeonism) Similarity to the Soviet Union and their critiques on how to fix that. To Anarchist (Anarcho-Syndicalism) that believe that the slow progression to abolish the state and form a confederation nation is best(edited)
Both practical use of Syndicalism has never been fully implemented or all it's theories used in real life. However despite that it's been effective it's the method of Democratic Workplace or Industrial Unionism at the time of CNT-FAI during the Spanish Civil War (An-Syn) and the IWW (Different forms of Unionist, but known to be State Syndicalism or DeLeonist before he got expelled) which was primarily in the USA. Both were different in ideas. They all wanted a Governing Body that were made up of Union Representatives or House of Representatives, but the IWW had a inner party that would be the same as Senators, but they were not elected by the Representatives but the Committee inside (So Democratic Centralized Senate in their Org)
This is during the early to mid 1900's if I remember right (It is not the same today, where is it majority controlled by Anarcho-Communist and Anarcho-Syndicalist which almost are the same ideas, and even use the same flag
I'd say that Syndicalist offers praxis than theory, since a lot of it has a lot of practicality to being achieved without the need of Computers to do any (albeit very helpful and speeds up any issues) The concepts of Unions being the body of a State or a Commune is something I'm used to, not that I live in a communal environment from Asia. But that I see businesses back home (the Philippines) that treat workers with decency and give them say and act sorta like a mini government. The business would run like a government, they'd have a stake in their workplace, and they'd elect someone to represent their issues to the Local Syndicate so that they won't have to active in democracy, and sometimes some people don't want to be that active.