There's lots of confusion about what to call various apple products.
Apple juice can be the imported re-constituted stuff from the big box store, more natural products like Simply Apple or the fresh product sold at your local orchard called cider. Cider in the US could be fermented or non-fermented, while in the UK the term cider is reserved for the alcoholic drink.
For brewing recipes I believe apple juice is a better term to use and then its up to the individual what actually goes into the brew.
A few years back I did a bunch of trials using different blends of apples and different yeasts along with some commercial juices and invited friends for taste tests of the samples. I was surprised to find that Simply Apple from the grocery store, scored near the top and although somewhat pricey, save a lot of time and effort compared to searching for heirloom apples, grinding, pressing and all the clean up.
Cheap juice from Walmart scored at the bottom, and local cider from an orchard was somewhere in the middle.