Condo--you own the space within the four walls, and a portion of common area. You own real property, and your mortgage is for that real property.
Co-op, you own shares (basically stock) in a corporation which owns real property, and as a benefit of you share ownership you are entitled to occupy a certain amount of space in the building, and are entitled to use of common areas.
Co-ops are generally much harder to get finiancing for (except in NYC) and that financing generally carries a higher interest rate because you aren't getting a mortgage. You are getting a loan secured by shares of stock in a corporation. The corporation holds the mortgage, not the individual unit owners.
Hope that helps.
Anne