There are significant differences between a condominium and a cooperative, but each is considered a common interest development or CID. The terms 'co-op' and 'cooperative,' are short for 'cooperative housing project.' Cooperatives were in existence and common before the condominium type of ownership was fully developed in the United States. They were especially common in New York City and the northeast.
In a cooperative the building containing the residential units or apartments is owned by a 'cooperative housing corporation. When you buy a co op you buy shares in the housing corporation.
In a condominium, each unit owner owns an individual apartment in fee simple. In addition, the buyer owns an undivided interest in the common elements such as the exterior walls, roof, any recreational things like pools, tennis courts and other areas.
Both condo and co-op owners have monthly maintenance fees to pay, but they can vary, depending on what expenses the fee covers.