I don't have much to say regarding Speed vs. Sped since the former seems to be more common as xenal said while the latter is more correct grammatically as Nevo pointed out, I don't know which one makes more sense to use so let's see if other people have something to add.
As for the distinction between Nightcore and Spe(e)d Up, I checked several ranked maps with these markers (both new and old ones) and apparently it's not true that only Nightcore Mixes have a higher pitch, most Speed Up Ver. songs do too. So technically they're both the same thing with the only difference being that Nightcore is usually more common on electronic songs, but many old maps use (Nightcore Mix) for non-electronic songs too, probably because on YouTube everything is labeled as Nightcore and the metadata rules weren't as strict back then. It would be nice to hear what mappers who mapped this kind of songs think about it.
As for the distinction between Nightcore and Spe(e)d Up, I checked several ranked maps with these markers (both new and old ones) and apparently it's not true that only Nightcore Mixes have a higher pitch, most Speed Up Ver. songs do too. So technically they're both the same thing with the only difference being that Nightcore is usually more common on electronic songs, but many old maps use (Nightcore Mix) for non-electronic songs too, probably because on YouTube everything is labeled as Nightcore and the metadata rules weren't as strict back then. It would be nice to hear what mappers who mapped this kind of songs think about it.