What's the difference between Cooperativism (the replacing of Capitalist firms with worker co-ops like Mondragon), Market Socialism, and Syndicalism? Given that they're all systems where workers democratically control the means of production, what's the difference?
There are several differences between these systems, but I think the best way to show said differences is to describe each system:
Cooperativism, as you said, is having workers democratically control businesses. However, unlike syndicalism and market socialism, cooperativism is not necessarily socialist and can still exist in capitalism. Platform cooperativism, for example, is a business model from of cooperativism that has been implemented by multiple businesses in capitalist countries. Even a society that fully implements this system can still have businesses that are all cooperatives while allowing people to privately own land and small-scale means of production, allowing this system to be implemented in capitalist and distributist economic systems.
Socialism is, by definition, "an economic theory or system in which the means of production, distribution, and exchange are owned by the community collectively, usually through the state." Market socialism is implementing this kind of system with a market economy. Under a market economy, all of the means of production and private property are owned by the state, a cooperative, worker's council, or some other form of social ownership by the community. As Paul R Gregory put it in his book Comparing Economic Systems in the Twenty-First Century:
"It is an economic system that combines social ownership of capital with market allocation of capital...The state owns the means of production, and returns accrue to society at large."
Market socialism has various different versions that correlate to this principle of collective ownership on a market economy from "pension fund market socialism" as described by William H. Simon in his book "Prospects for Pension Fund Socialism" to Ricardian socialism (a version of classical market socialism created by economist David Ricardo).
Syndicalism was a form of socialism where the means of production are controlled by a series of workers' unions who decide how the means of production and personal property are divided, not necessarily utilizing cooperatives. While Syndicalists may have some form of government, they are generally against any form of a state and see it as a tool of oppression - something market socialists and cooperativists don't necessarily agree with.