In general terms: A co-op is a corporation that owns real estate. If you belong to a co-op, you own stock in the corporation and the exclusive right to a given unit. There is usually an underlying mortgage on the property and your co-op fee includes some or all mortgage payments as well as other costs.
With a condo, you own real estate and you have access to certain common facilities. The condo is typically responsible for exterior maintenance and you pay a monthly condo fee. You have your own title and mortgage, so mortgage costs are not part of the condo fee.