Cider is unfiltered and untreated. It is really just what comes out of a apple press. Therefore traditionally it has a much shorter shelf life. The biggest traditional difference is that the cider is not vacuum sealed or pasteurized. But today they are. So the difference today depends on the products.
cider is a beer. it has more gasses elements in it. It has more spices and it more powerful to drink. Juice is flat that you can see through because of the less spices nature has for the apples. It is sweet and it can also have a smell of a gas but it is not harmful.
Fresh cider is non-alcoholic, fermented or brewed cider is alcoholic and only sparkling cider is "gassy". Sparkling cider is usually non-alcoholic and the fizz is from a process not unlike the process of adding fizz to soda pop (carbonation). Cider can have spices added, but not all do. Also cider is usually a seasonally available product, available during apple picking season (Autumn).
What the difference is, apple juice goes through a process of repeated straining to get a clear product. Cider doesn't go through that straining, so when you see it in a bottle it's cloudy. Cider can, if it's aged long enough, ferments and becomes alcoholic.
The difference between apple cider and apple juice is that apple cider is raw since it goes through a process of no filtration of squeezed apple. Apple juice is filtered making dirt or other matter removed and this makes it stay fresh for longer.