Difference between house and computer symbols in Finder

The computer icon point to the root of the machine. You can see all connected drives from there.

The house points to your home directory.

The house symbol is your home login folder. That's the folder which contains your stuff, and your other local folders.

The computer symbol (depending on which one) can either be the root of your file system, or can be a network share, which can be another computer, or network storage, or even sometimes a printer with an embedded storage server.