There is a lot of overlap.
"House" emphasizes the idea of a physical building.
"My house is made of wood."
"We replaced the windows in our house."
"If it rains a lot, my house gets water in the basement."
"Home" emphasizes the place where someone lives.
"I feel sorry for children whose parents have to move, I loved being able to grow up in one home."
"Our grandchildren are coming to visit us at home." "I love how you've decorated hour home."
Real estate agents always call houses "homes" because it makes people think about happy feelings rather than leaky roofs.
A famous, sentimental, beloved poem by Edgar Guest goes like this--I think I'm going to "fix" the spelling a bit:
"It takes a heap of living in a house to make it home."
("Heap" means "a lot").