Most gravy in the US is brown gravy, which is, I think, the same on both sides of the pond. It’s made from meat broth (usually beef or turkey, or whatever the meat is with your meal), generally thickened up with some sort of starch. It may also contain gibblets (poultry organs) or bits of actual meat. This is the stuff which is generally served over mashed potatoes, meat, or stuffing.
White gravy is made primarily from sausage fat, and will generally leave an uncleanable layer three inches thick in the bottom of the pan when you’re done. It’s the gravy generally used for biscuits and gravy and country fried steak. At places which serve either of these dishes, white gravy might also be used for mashed potatoes: This is often the case at fried chicken places.
Incidentally, country fried steak (also called chicken fried steak) is a way of making cheap cuts of meat palatable. You take your steak, tenderize the hell out of it, bread it, deep-fry it, and then serve it with a side of mashed potatoes and white gravy over all of it. Along with meatloaf, it’s one of the two primary staples of diners and truck stops.
There’s definitely a difference between apple juice and sweet cider in the US, but nobody seems to agree on what that difference is. Generally, if you buy it at a roadside fruit stand out in the country that grows their own apples, it’s cider, while the big-brand juice box stuff is apple juice. In any event, if it’s fermented, it’s hard cider, and if it’s fermented and then further distilled (most often by freezing), it’s apple jack.
And I didn’t know that Brits had dumplings (Americans have those too, and they seem to be the same thing). That makes biscuits much easier to explain, since they are, indeed, essentially the same recipe.