This http://en.wikipedia.org/wiki/Apple_cider has a definition and pictures of American apple cider and apple juice. In the US, apple cider is sold in the autumn and I presume that fewer preservatives in it than in apple juice. Apple cider has a short shelf-life. Apple cider is cloudy, like orange juice with pulp.
The labeling on your “apple cider” is clearly wrong, even by US standards. Those bottles of apple juice will probably last forever. Better to dump that crap down the drain.