So basically all cider is aple juice, not all AJ is cider. Except in you are in the UK I do believe all cider is fermented?
Alcohol is either distilled (hard liquor) or fermented (beer/wine/cider/graff/mead etc). So all cider is fermented to one extent or another.
At least here in the US in the apple juice vs apple cider discussion it's usually simple to tell which is which in the un-fermented versions.
Ciders are unfiltered first pressings from the apples, are cloudy, can be pulpy and may or may not have been pasteurized. Cider's also traditionally have nothing, or vitamin C added as a preservative.
Apple juice traditionally is always filtered, though some are labeled apple juice and are unfiltered. Apple juice may or may not be from concentrate and may have additives for preservation.
Further, Cider's sometimes are sourced from specialty apples, vs the more commonly grown mass produced apples and can have a very different taste.
For example I live in Sonoma County, CA near Sebastopol, CA a region that was famous for growing Gravenstein apples in the 19th and early 20th century. The Gravenstein apple is a tart apple that is used primarily in cooking & ciders, has a small picking window (July - Aug) and doesn't preserve well so it must be used in that season. Sadly most of Sebastopol has caught the "wine country" bug and have removed orchards to vineyards as the $ per ton is higher. There is less than 5 growers and only 1 comerical processor left in Sonoma County and less than 20k tons are produced annually.
Tying that back in to taste is this. I could have a glass of tree top, a glass of motts and a glass of generic brand apple juice and notice very little difference except they're all overly sweet. But a good cider (especially a gravenstein based cider) has a very distinctive taste, and while almost $7/gal is what I choose to use as a hard cider base if I'm not worried about a crystal clear cider.
Hard Cider's further murky the issues. I don't know how commercial brewers do it, though I may ask next time I'm in the local cider pub. Homebrewers however make a hard cider out of both cider and apple juice and seem to make the decision based on material cost and desired clarity.