There is a difference between condominiums and co-operatives. Both are a type of multifamily properties that house multiple units. Condominium owners actually own real property, while co-op owners have shares that give the right to occupy and use the unit.
A co-op can be thought of (because it is) a corporation formed to own multifamily residential property. Residents own shares in the corporation which owns an entire group of residences - usually one or more apartment buildings. Co-op members do not own their units. Instead they make an investment in the co-op and have a voice in controlling the its activities.
In general, condo owners are subject to fewer rules than co-op apartment owners and, spend less time in internal governance. A condominium, carries with it joint ownership of common portions of the property, while other areas are owned privately.
financing a co-op can be a little tricky. A newly formed co-op takes usually takes out a single large mortgage on the entire building and then the owners buy shares of stock that entitle them to a proprietary lease to occupy a unit within the building. As the co-op ages and equity increases, the value of each unit increases, and future buyers might be required to pay in cash or finance as much as 50% or more.