@tanguatlay,
A house is a physical structure, a building, or some sort of edifice made of bricks, mortar or possibly wood. There's no implication of any relationship of the potential human inhabitants.
A home has a social meaning and it can be a collective or even be a group of people located (but not exclusively) in a house. There's an implication that it may contain a family or some social group, for example (but not exclusively), a home with a mother father and children, or orphans or the disabled.
Being at home, means feeling those social feelings and cues of having the familiarity of possibly one's companions, belongings and security. So, as an example, one would never say, "I'm 'at house'."