In a "condo" arrangement, you legally own a particular unit in a multiple unit structure of building. Plus, under a typical arrangement, you have a share and a right to use common property (i.e., hallways, elevators, gardens, swimming pools, club house, and so forth) within that structure. Monthly payment to an "association" for expenses incurred in maintaining the common property are normally required. The association gains its legal authority from the legal documents which create it - declarations, by-laws, and articles - and these associations typically run like a corporation and may be managed by professional property management companies. There are usually complaint and appeal processes built into the association documents to protect individual rights and to provide a mechanism for resolving controversies within the community - as well for selecting the members of the Board of Directors who oversee management of the association.
A "co-op", on the other hand, is a "horse of a different color". You do not own your own specific unit in the building but own stock in the corporation that actually owns the building and all the apartments. You lease your apartment or unit from the corporation. The unit’s size determines the number of shares of stock you must purchase. Monthly fees based on the number of your shares of stock are assessed for the mortgage payment, taxes, and general operating expenses. As a shareholder, you have a say in electing the Board of Directors who manage and decide on how the cooperative is to be run, who is qualified to buy shares, and so on.