Both are forms of multiple ownership.

Co-ops or a cooperative apartment is a form of ownership in which a corporation is established to hold title of a property and lease the property to the corporation's stock holders or shareholders. Occupants of the units sign a subscription agreement for stock and receive a propriety lease on a specific space or unit. Even though the shares in the co-op are not real property, the shareholders are entitled to deduct mortgage interest (I am not a CPA and do not know the ins and outs of tax deductions).

Condominiums are a form of ownership of individual units in a multi-unit structure or building. The owner of each individual unit has co-ownership of the common areas or common elements. The framework of this ownership is established in the master deed.