'Haus' is 'house,' and is a building built for permanent living in that is distinct from an apartment, hotel, or other living accommodations. A house is a house even if nobody lives there; it's just the building.
'Hause' is 'home,' and is a specific place someone or something lives. It doesn't even have to be a house to be your home. A rabbit's burrow is its home even though it's not a house.