While cider can be made from the apples you find down at the local grocery store, a good cider is not usually made from just these desert apples. To get a much more interesting cider apples of different styles are blended together to give character, complexity and body. "Cider Apples" fall into one of four categories based on the proportion of acidity to tannin.
One would think that sweet refers to the apples that have the highest levels of sugar, this is not why apples are categorized as sweet. Sweet apples have low acidity and low tannin. these apples are usually blended with other apples that are very high in tannins or acidity to help neutralize some of the sharp and/or bitter flavors, but to much sweet apples will result in a very bland hard cider.
Sharp apples are ones that have high acidity and low tannins. Many North American desert apples fall into the sharp category. The acidity gives the apples a crisp flavor. Sharp apples are often used in commercial sweet cider blends to give the cider a fresh crisp taste when the acidity is combined with the high sugar content. The problem with fermenting many of the commercial sweet ciders is once the sugar has all been converted to alcohol there is no more sweetness to balance out the acidity resulting in a hard cider that is far to sour for most people.
Bittersweet refers to apples that are relatively high in tannin but low in acidity
Bittersharp apples are ones that are relatively high in both tannin and acidity