grammar

First, it helps to ask a question. Otherwise, we are left guessing as to what you want to know. Let me take a guess.

No, the correct spelling of "house" is not "home". Is that what you wanted?

Second, house and home have very different meanings. There are many, many houses, but you have only one home. And what is your home is only a house to me.

House -- A building for human habitation.

Home -- The place where one lives permanently

I hope this helps.

What is the context? You could leave your home and it might not be the physical component- like leaving home for the first time you are referring to not just the physical house but your town, family, friends, etc. Leaving the house would be more on a literal level- leaving the house to go to the store. Leaving the house is more temporary than leaving home.