house is hus. Jag äger ett hus. ett hem is "a home" (hemmet is "the home"). I don't see the noun "hem" used much but it is used. hem usually means "going in the direction of home". Jag åker hem. Han kommer hem imorgon. hemma means "at home". Jag stannar hemma. Är du hemma? Ska du va hemma kl 4?
I noted bort and borta because it's the same pattern. The word with the "a" on the end is usually the place, and the one without the "a" is the direction.