Most startup employee recipients of options never get to exercise them for various reasons, often unable to due to cash flow or restrictive timing reasons, or because they aren't profitable (the employee would take a large financial loss). Many of those who do exercise the options get their shares after leaving the company or they're about to leave. And finally, of the small subset of employees who have shares as a result of exercising while still employed, the number of shares they have is a tiny percentage even in aggregate, so they have effectively no influence at shareholder meetings, if they choose to attend, and if their shares have voting rights which they don't always have.
In co-operatives, the majority of shares as well as voting rights are usually held by a high proportion of employees, so that's a completely different dynamic. As well as voting rights, it means any profit distributed as a dividend tends to go to employees as well.
But the rest is more or less correct even when the options mature and you can exercise them you usually do not get voting rights it’s nearly always restricted shares.
Also note that unlike cooperatives there is also quite often restrictions on how much stock you can own as a regular employee in a public or even private company the employee shares in cooperatives usually have a different legal framework than regular company shares.
One of the key differences is quite often as someone already mentioned is that shares in cooperative grant a single voting right to a shareholder rather than per share.
You can also have some more complex tiered holding structures such as where all the employee held company shares are issued to a single entity that represents the employee shareholding collective and that entity then grants a single share to each employee, alternatively other models than direct shareholding can be used such as trusts where the trust holds the company shares and the trustees get voting rights.
Also, there's some significant differences in how shares work between cooperatives and corporations (at least in Germany, where I live). In a corporation, you get one vote per share, and shares can be freely traded once given out. In a cooperative, you only one vote per shareholder, no matter how many shares you hold, and shares cannot be traded. You can invest into the cooperative to get shares, and you can return your shares to get your capital back, but the cooperative gets final say in who gets to hold shares.
A employee stockholder plan is one dollar one vote.