A baby bath is a special, small bath just the right size for washing a small baby in. It is easier to wash a baby in a small bath on a table than in a regular bath.
A bath is a large container you can fill with warm water and sit in to wash yourself. Baths are very relaxing and are wonderful if you are feeling sore.
A hearth is the floor of a fireplace. The hearth usually is larger than the fireplace, and makes a small step in the front of the fireplace. It is there to protect the floor around the fireplace from burning embers.