All private companies have shareholders. The shares they own are just not publicly traded shares. "Shareholders" is, in this context, the same as "owners," and all private companies have owners.
So, what's the difference between a coop and a private, for-profit company in which everyone who works for the company owns the same portion of the company and gets an equal say in decision making? Not much practical difference, really, although with a coop, those things are enshrined, whereas with a private company, they're optional.
> So, what's the difference between a coop and a private, for-profit company in which everyone who works for the company owns the same portion of the company and gets an equal say in decision making?
Initially that would be effectively the same, but in a coop the equal ownership by all employees (and only employees) is also supposed to stay that way through employment changes: if a person quits the company, they don't take an equity share with them, or they'd become an outside investor. Instead the company is equally owned at all times by the current employees.
It might be possible to write up a complex contract that does that with regular shares, forcing people to hand them in if they quit the company (and prohibiting sales), but since regular shares are considered property there are a lot of pitfalls around making that work (if it's even possible), along with opportunity for shareholders to challenge the structure. A coop structure avoids that issue by not having regular equity shares in the first place.
So, what's the difference between a coop and a private, for-profit company in which everyone who works for the company owns the same portion of the company and gets an equal say in decision making? Not much practical difference, really, although with a coop, those things are enshrined, whereas with a private company, they're optional.