Student or Learner
Is there any difference between the three phrases with 'home'?
1. I stayed at home last night.
2. I stayed in the home last night.
3. I stayed (at/)in the house last night.
The are often, but not always, differences in meaning between "house"
A house is a physical structure. It a builing in which one lives, works,
or carries on other daily activities.
Home is often used as a synonym for house but it can have a much broader meaning. as well.
Home can simply mean the place where I eat, sleep and share with the rest of my family or friends be it a tent, a boat or even just a space on a city street or in park.
Grammatically 'home' and house' are treated a little differently:
I can go to my home' but usually I will just 'go home.'
I can go to my house but I cannot 'go house.'
In your examples:
If I stayed at home I mean that I stayed at my home.
If I stayed in the home it must mean I stayed at someone else's house.
(This sentence doesn't sound very natural however.)
If I stayed 'at' or 'in' the house it would mean someone else's house.
If you mean your own house you would say
I stayed at (or in) my house last night.