I'm not native but from what I heard - a house usually implied to someone's home (one family) and in the US sometimes even more strictly applied to a separate few-story residential building that belongs to a family, a house usually stays on a piece of land that belongs to the same family . Other types of "residential spaces" will be townhouse, apartment, flat, studio and condo (from condominium).
Other types will be buildings and one building can include several apartments for example.