A home is the place where someone lives. A house is a type of building. A person's home could be a house. Or it could be an apartment/flat, a mobile, or other types of buildings. The grammar for the two words can be different, sometimes. If I am talking about going to my home, I would say: "I'm going home" (there is no preposition or article like 'a' or 'the'). If I am going to my house, I would say "I'm going to my house." Same thing if I want to tell someone I am already there. I would say: "I am home" or "I am at my house."