Most "co-ops" are customer co-ops (Credit Unions, for example, are owned by their members, most grocery co-ops are membership programs, REI is/was the same). Farmer co-ops are owned by a collection of farmers, to pool resources for selling to consumers, but most employees aren't co-owners. Worker's co-ops are rarer, but you find them in the taxi industry pretty often, and in home care.
Today I learned. Thank you!