A person who enjoys spending time at home is called a homebody. A homebody can still have a good time going out with friends, and enjoy other aspects of a normal social life, but prefers to be home. Homebodies may like to be alone, or with family at home, or have friends come over. They don't avoid other people.
A hermit prefers to be alone and live a simple life away from other people, sometimes for religious reasons.
A recluse is someone who lives alone and avoids other people.
A shut-in rarely or never leaves home usually for medical reasons.
I hope this helps.