A condo is a type of legal ownership. A homeowner owns a separate interest in an individual unit plus a proportional interest in the common area of the development. Generally, the unit owners own, maintain and insure the living space inside their home and the association takes care of the rest of the complex including exterior walls, roof, pool, etc. The specific ownership elements are defined in the condo documents and should be reviewed by a buyer prior to closing.
Townhome / Townhouse:
Townhome is an architectural style with multiple floors and common walls but no neighbors above or below. They can be owned as condos or as individually owned structures including the land below them. If individually owned, the owners are generally responsible for their specific building insurance. An owners association may be responsible for common areas (landscaping, driveways, etc). HOA dues are usually lower for townhomes vs similarly priced condos.