This is as good an explanation as any other one I've read, about the difference between a condominium and co-operative apartment.

It's not that important, to those of us who buy, in Boston, because almost every building is a condo. There's only a handful of co-ops in the city.

Question. What is the difference between a mortgage on a condominium and a share-loan on a co-op?

Answer. [T]he difference lies in the type of property that is used to provide security for the loan. Since a condominium is real estate, a mortgage provides the lender with a security interest in real property. And since a co-op owner owns shares in the co-op corporation that owns the building – and has the right to occupy a specific apartment – a share-loan provides the lender with a security interest in personal property consisting of shares of stock in the co-op and the proprietary lease for the apartment.

More: Condo Mortgage vs. a Co-op Share Loan - By Jay Romano, The New York Times