Apple Cider is the expressed juice made from the maceration and pressing of apples. When cider is treated by some method to prevent spoilage while in airtight cans or bottles, it is marketed as apple juice in most countries.
|Processing||Apple cider is created by the maceration and pressing of apples.||Apple juice is created by the maceration and pressing of apples.|
|Fermentation||Apple cider can be fermented to make hard cider.||Apple juice is not fermented.|
|Clarification||Apple cider is not clarified. This means that the apple cider still contains its starches and pectin, giving it a darker, cloudy appearance than apple juice||Apple juice is further treated by enzymatic or centrifugal clarification.|
|Pasteurization||Apple cider may or may not be pasteurized. Unpasteurized apple cider has a shorter shelf life than pasteurized apple cider.||Apple juice is pasteurized before bottling. Pasteurization prolongs shelf life.|
|Health benefits||Reduces the risk of heart disease, helps in preventing cancer and improving cognition. High sugar content may lead to weight gain and increase the risk of diabetes.||Reduces the risk of heart disease, helps in preventing cancer and improving cognition. High sugar content may lead to weight gain and increase the risk of diabetes.|
|Calories||120 calories and 2 calories from fat in 8 fl oz.||120 calories and 2 calories from fat in 8 fl oz.|
|Carbohydrates||~9% of daily value(28g)||~9% of daily value(28g)|
|Sugar||~8% of daily value (24g). May also contain added sugar.||~8% of daily value (24g). May also contain added sugar.|
|Vitamin C||5-6% of daily value.||5-6% of daily value.|
|Iron||5-6% of daily value.||0%|
|Calcium||2% of daily value.||0%|
|Potassium||~4% of daily value(135mg)||~4% of daily value(135mg)|
|Sodium||1%-3% (10mg-60mg) of daily value.||May or may not contain sodium.|
edit Preparation Method
On the other hand, apple juice undergoes an enzymatic or centrifugal clarification. During this step, the starch and pectin are removed. Pasteurization follows as a final step before bottling. Apple juice is bottled in glass, plastic, or metal containers for use by the consumer. The entire process from apple to juice gives apple juice a longer shelf life than apple cider. Here's a video on how apple juice is made:
Apple cider may be made into hard cider through fermentation.
Apple juice is one of the most popular juices in the world. It is almost always commercially made due to the sheer cost of manufacturing a clear juice. Apple juice is enjoyed year round and is widely available. Usually, apple juice is served cold.
Apple cider is a popular drink around Thanksgiving, Christmas, and other fall and winter holidays. Apple cider is often made on the farm, but can be manufactured. When manufactured, the drink is pasteurized. When made at home, the drink is unpasteurized. The shelf life of apple cider is limited. Fermented or hard apple cider has a longer shelf life than soft cider. Apple cider is served cold or warm.
Both apple juice and apple cider may be concentrated. Concentrated apple cider lengthens the shelf life and makes the drink available in the off-season as it allows the cider to be in a frozen state for use at any time.
edit Nutrition and Health Benefits
Both apple juice and cider are excellent sources of Vitamin C. They are very low in saturated fat and sodium (10mg). They have no cholesterol, thereby reducing the risk of heart disease. Scientists from the American Research Center US Apple Association discovered that apple juice and cider can protect from certain cancers (the pectin and polyphenols in apples have an anticarcinogenic effect on stomach, preventing the development of tumors). They are also know to protect against asthma and brain cell damage. They also contain iron and have a tendency to withdraw kidney and gall stones. They also helps with dysentery, laryngitises, paratyphoid fever and acute respiratory diseases, by leading the heavy metals and radionuclides salts out of the body.  A research at University of Massachusetts−Lowell revealed that apple juice and cider have very powerful effect on brain functions and hence may improve cognition. 
You can find current prices for apple juice on Amazon.com. Manufacturing and selling untreated cider is less common but you may find some products on Amazon.