A "house" is a type of building for people to live in. "Home" is where you belong and feel comfortable.
When speaking of movement towards "home" there's no preposition.
- I'm tired. Let's go home. Let's go to the house.
When there is no movement use the preposition "at" or no preposition at all.
- All the lights are off. It seems like there's nobody (at) home. There's nobody in the house.