Cider is the hard stuff. Crushed apples with minimal processing. Because it can ferment, it is usually found refrigerated. Apple juice can often be found elsewhere in stores, where it can remain stable.
Which you should buy comes down to personal preference. Typically, though, recipes calling for apple cider should use apple cider. Processed juice may be too sweet an ingredient.
Apple cider is raw, unfiltered juice - the pulp and sediment are intact. To make cider, the apples are ground into an applesauce-like consistency, then wrapped in cloth. A machine squeezes the layers and strains out the juice into cold tanks. That’s the cider that ends up on store shelves.
Apple juice, on the other hand, takes things a step further - removing solids and pasteurizing the liquid to lengthen its shelf life. It’s typically sweeter, possibly with added sugar, and may lack the stronger flavor of its relatively unprocessed counterpart. It is also often lighter in color, since the remaining sediment of cider can give it a cloudy appearance.