The fruit from Malus pumila, apples are thought to have originated in the Caucasus mountains.
Almost every apple we use today is grown from a graft rather than from seed. Despite the fact that modern, store bought apples are chosen for their ability to endure cold store and endure transport it is still possible to find apples that have been grown since the sixteenth century and even earlier.
These are the apples most people are familiar with. Some are appropriate for eating raw, others for cooking or turning into applesauce.
These are usually grown for their aestheic appeal as the apples produced are small and often sour. Crab apples can, however, be used to make a jelly.
In general there is more than one type of apple used for cider, and crab apples and eating apples commonly find their way into a bottle of cider. There are some apples though which are only used for brewing.