Adapted from is like created using different media. Think what anime adaptations or movie adaptations do. It is supposed to match the original as closely as possible, but realistically it doesn't always work out like that.
Prequel and Sequels are stories that respectively precede or follow the events of some main story, typically with the same characters but unrelated plot. If plot of each volume is distinctly separate, it can also be used for consecutive volumes of a single series (like the 1st and 2nd are prequels to the 3rd, and 4th up are sequels).
Side story is a separate story set in the same world. May be connected to the main story through characters or events, but can also be completely unrelated and instead expand on worldbuilding. As the name implies, it's relatively short.
Spin-off and Alternate Story are similar, both describe what would have happend if the story was different in some ways. They may be very similar, but can also diverge completely at some point. I believe the difference between Spin-off and Alternate Story is that the latter does not interfere in the worldbuilding and established lore, instead pulls the story in a different direction from the same starting point. A Spin-off can do a lot of things, up to things like a completely different world but same characters or vice versa.
Shared Universe does not specifically refer to one story, it can be used to group together stories that exist in the same Universe. There is usually one original story, but it's not necessary.
Main story I believe is the base for some distinctly separate Sequels, Prequels, as well as Short stories, and perhaps some vaguer cases. On Scribble Hub specifically, I think this is supposed to be used to indicate that the story is not standalone, but to be honest I've never seen anyone use it.
Note that, on Scribble Hub, you're making references with those tags. If you make a sequel, you tag the main story as a prequel in its description, and you tag it as the sequel in the main story's description.