Let me see if I can answer. I've made applesauce, apple butter, spiced crabapples and apple jelly
First, you asterisked apple preserves but didn't finish so I'm not sure what you consider apple preserves. Candied? Apple jam?
Anyway, applesauce is the easiest. You chop up a bunch of apples, add some sugar and/or spices, cook until the apples are soft. Smash a little or a lot . . . Boom! Applesauce.
Apple butter is similar to apple sauce except you tend to cook it longer to get more of the liquid out so you have a denser, more intensely flavored spread and you'll probably want to puree or smash it so that the texture is smoother.
Spiced crabapples are cooked whole, in their skins with the stem attached. You cook them in a sweet/sour syrup and pack them into a jar much the way you would make pickles and that syrup becomes the preservative.
Apple jelly is a completely different beast. You cook your skin-on apples (skins are where the pectin comes from) until soft then, WITHOUT PRESSING OR SQUEEZING, allow the juice to drip through cheese cloth for several hours. This is all about achieving maximum jelly clarity. Once all the juice that's gonna drip through has done so, you begin a gentle reduction until it becomes golden. This is remarkably labor-intensive although the jelly can be used on its own or as a pectin substitute.
Synchronistically, a by-product of making apple jelly can be apple sauce or apple butter. You put the leavings through a food mill and proceed from there to make sauce or butter.
Hope this helps.