It refers to type of ownership.
In a coop, each owner owns shares in the corporation. The shares entitle a person to occupy a specific unit. However, the corporation is the owner of the building. And that includes the unit you're living in.
In a condominium, each owner actually owns his or her own unit. In addition, there is a condominium association, composed of all the owners in the condominium. The association will own the common areas--for instance, in a large building that'd include the lobby, the elevators, and the common grounds.
As a practical matter, a coop imposes more restrictions on buying and selling, since the coop (through its board) can make a decision whether or not someone can buy the shares that would, in turn, entitle him/her to live there. In a condo, if you and the seller agree, you just buy the place.
One other point: "Condo" and "coop" have nothing to do with the physical structure of the building. Many people think of condos or coops as tall building, like converted apartment buildings. Some are. But you can have condo or coop garden apartments. You can have condo or coop townhouses. And you can even have condo (and I guess coop) single-family homes.
Both coops and condos can be pretty restrictive in what you can and can't do. It all depends on who's serving on the board. I've lived in a number of condos (no coops), and they've ranged from dictatorial to relaxed. One tip: Make sure you read the rules and regulations and other condo (or coop) documents before buying.
Hope that helps.