There are a great variety of co-ops. If you define renting narrowly enough, then they are of course different. But the point is that for some (and the co-ops I've seen personally) you don't have to make a down payment for a mortgage like you do with a condo or house. You instead pay a monthly fee that covers the co-op's mortgage/repairs/taxes. Or if the place is fully owned by the co-op, then just the repairs/taxes.

But you retain the flexibility of renting in that you can leave reasonably easily since you're not personally responsible for the mortgage.

I think there are also co-ops (possibly more commonly) where it's essentially just a condo where the building is collectively owned by the tenants instead of a for profit company. In that case, it's much less like renting.