you're describing bolshevik/bismarckian state 'socialism', a conservative compromise/trick/ratfucking that generally starts by executing all the communists, like the bolsheviks did. bismarck specifically talks about how he did this on purpose to keep actual communism from blooming out of these huge mutual aid projects that were happening.

the short version is: the workers own the means of production. individually or collectively. so the steel workers own the steel mill. the seamstress owns her serger. the plumber owns his wrench and snake. just that, and it all exists for the good of everybody, with everybody acknowledging that they can't do it on their own, or offering a lot of public entertainment by trying to.

there's a bunch of forks from there, and ways to make this function and eliminate the frictions, but that's all communism is. some proposals still even include markets (though im not a fan), some are regional, some federated in a bunch of different ways, some are centralized, some are radically decentralized, some are 'return to monkey', some require cutting edge technology for communication and collaboration (a cool example of that from the 70s is called cybersyn, which was, like, kick starting the star trek future in chile before everyone involved was hunted down and killed by CIA proxies, except two guys who were out of the country, one of whom was literally taping a debate about it for the CBC at the time, which got REALLY awkward for his conservative opponent)