A worker owned co-op is the very definition of the workers owning the means of production, that is Socialism. While Capitalism is all about the owner with capital owning the means of production.
But yeah, there are a lot of places that call themselves a co-op but really aren't. They may have started out as a co-op but then turned into a corporation owned by the original workers who started the co-op.
There comes a point in a co-op's development where the original workers who put their money into the business have to decide how, or even if, they are going to incorporate new workers as owners too. But if they just let all workers in as owners who receive part of the profits, without any method to pay-in an equal share as the original workers, then the original owners frequently bulk and pull out.
But there are ways to buy into a co-op where even the most impoverished person can pay in their fair share.
If the co-op decides not to let any new workers in as owners, with equal voting shares, just hiring like other corporations, then it basically just becomes a regular corporation owned by the original workers. That's where the confusion comes in.
But yeah, the original concept of workers owning the business, the means of production, is socialism at work.
There are a lot of examples of socialism throughout the US. Social Security is socialism. Some say our current government is socialism for the filthy-rich. Despite what the filthy-rich propaganda would like you to believe, there is socialism in the US, we are not 100% capitalism. But then no country is 100% of any economic form.