The Sleep spell explicitly causes targets to fall "unconscious" but includes many references to sleep, as well as the line:
"Undead and creatures immune to being charmed aren’t affected by this spell."
The Eyebite spell, on the other hand, states, as one of its options:
"Asleep. The target falls unconscious. It wakes up if it takes any damage or if another creature uses its action to shake the sleeper awake."
Although the name of this effect is "Asleep" there is no text in the Eyebite spell that indicates that creatures who do not sleep are immune, as in the Sleep spell. (I suspect that specific over general likely means that this Eyebite effect doesn't work on elves, but that's not really part of this question—I'm just providing context for the ambiguity here.)
The Dream spell states:
"If the target is asleep, the messenger appears in the target's dreams ..."
Once again, it includes a line indicating that creatures such as elves are immune.
The "Unconscious" condition of D&D 5e does not mention being asleep and there is no "Asleep" condition.
This question contains relevant discussion of whether elves can sleep, which I think mostly just muddies this question a bit more.
My question is whether there is a fundamental distinction anywhere in the rules between being asleep and being unconscious. Clearly elves can be unconscious without being "asleep," but can a human be unconscious without also being asleep? Given that the dream spell works on creatures who are "asleep" and not who are "unconscious" how can the DM tell if the creature I'm targeting is asleep or is unconscious-but-not-asleep? (Or: can I cast Dream on a human I just knocked unconscious and why or why not?)