The difference between “Home” and “House” is subtle, but they are very different. A ‘home’ is where a person or family lives.
A house is just a building.
If a family lives in a house then that house is their home. If they live in an apartment then that apartment is their home. If a place is your permanent residence then it is your home. A home is an abstract place, it is different to everyone. A student may live in the dormitory at university, but probably wouldn’t consider that a home. If someone lives alone in a small apartment they may consider that their home, or they may still consider their childhood home as their real home.
“I’m going home” and “I’m going to my house” can have the same meaning. If you live in a house.
“I’m going home” and “I’m going to my apartment” can have the same meaning, if you live in an apartment.
“I’m going to my friend’s house” is a common expression.
“I’m going to my friend’s home” sounds just a little strange. It’s his home, not yours.
Home country, homestay, homeowner, home schooled… ‘home’ can also be an adjective. It’s the place where you live, the place you belong, the space that belongs to you. ‘House’ is just a building.
We even have the expression “Make a house a home” referring to doing things like decorating, having kids, getting pets… anything to make the building feel like a home to you.