The main difference between lambs and sheep is their age. When you say that the animal is over one year, it is called a sheep. When the sheep is not yet one year old, you will call it a lamb. Lambs and sheep are both slaughtered by people for food although the wool of the sheep is sometimes used in order to create different clothes.
The meat of the lamb usually costs more because the meat is said to be more tender. The lamb is still required to drink the milk of its mother so that it can continue to survive as it is still young but the moment that it reaches one year, it will already be called a sheep.