En casa

English gets by with room and a modifier. Spanish has several words and expects you to pick.

Habitación is a room in general, and specifically a bedroom in a house or hotel. If you book a habitación doble, you are booking a double room.

Cuarto is also a room, and also a quarter. It is more colloquial than habitación and much more common in Latin America. Mi cuarto is my room in the way a teenager means it.

Sala is a hall or a large public room: sala de espera, waiting room. On its own, in much of Latin America, it is the living room.

Pieza is a room in parts of South America, a piece elsewhere, and a musical piece everywhere. It is the one to be careful with.

piso

Piso is a flat, in Spain. It is also a floor, in the sense of a storey: el tercer piso. And in Latin America it is the floor you walk on, where Spain would say suelo.

So está en el piso means it is on the third floor, or it is on the ground, depending on which ocean you are nearer.

casa is not always a house

Casa covers house and home both. Voy a casa is I am going home, with no article, and the missing article is what makes it home rather than a house. Voy a la casa is I am going to the house, a specific building.

Hogar is home in the warm sense, the hearth, and it is much rarer in speech than English home. It turns up in advertising and in the phrase hogar de ancianos.

The furniture is where the false friends hide

Mesa is a table, and it is also the desk you work at, which Spanish is happy to leave unspecified. Cama is a bed and nothing else, mercifully. Llave is a key, and also a tap in much of Latin America, and also a spanner. If someone asks you to close the llave, they do not mean the door.