What is that determines whether a certain sequence of motions is a "move" or a "combo"?

In some cases (the really basic moves), it's pretty obvious, but not always. Take, for example, fountains, or alternating arm wraps. A fountain has a bunch of more basic moves contained in it- weave, reverse weave, windmill- so it would make sense to just think of it as a combo. And arm wraps are basic moves, and an alternating arm wrap is really just a sequence of arm wraps, making it an arm wrap combo, no?

Perhaps the categories are not exclusive. Is it just that if a certain sequence gets to be widely-enough used and talked about, it becomes a "move" by popular consensus (my personal categorization system says "if there's a name for it, it's move; if you have to describe it, it's a combo")? Or is there something else going on?

a move is the established motion of a move like a weave foutain butterfly etc. but a combo is when you combine a different variety of moves to create your own combo. basically its a combination of moves.

Well, I kinda have my own naming system for stringing so you might not want to listen to this at all. But the way I see it... (for stringing mostly, not much poi) a move is like a certain motion that only one hand does kinda. Like a shotgun is one move, an arm wrap is one move, a neck trace is one move, ect. Then after that I think there are what I myself call hybrids. An example is doing a shotgun and a wrist flip trace on the same arm. To me hybrids are when both arms do one move each at the same time/ alternately. Another example is one arm does a neck trace while the other does a knee trace, or another example is a double bicep wrap. Then mini combos are next for me. That is when you put a very small amount of hybrids/moves together to create one small sequence thats only a few seconds long. Those mini combos are then put together to create what I call combos.

Lots of contemplation XD.

well a combo is well.. uhh you can't name it specifically cuz you linked and slapped a couple of moves here and there. string manipulations are mostly combos cuz you can't name each manipulation you make up .. xD

This is something that gets brought up from time to time, especially when people start throwing around names for what really is just a combo of smaller moves. You're right though, things like fountains and pirouettes are a combo of moves. In the case of fountains, it was already accepted as the name of a poi move so it was easily carried forward to stringing.

There are other combos that have been given names along the way. Some of them stuck and others have not. A great example that pops up a lot here is sun wraps - which are basically just dual bicep wraps that someone gave a name to. It seemed to stick amongst some crowds while others refuse to accept names given to every little combo that someone invents. I think the majority of people here lean toward the latter, preferring not to give a name to every combo out there.

I think your analysis was pretty much right:

Alternating arm wraps is definitely not a move. It's just considered the "first" (or fundamental) wrap combo most people learn.

A fountain is a poi combo. There's a bit of difference for poi since people with really good flow are essentially doing a combo the whole time they do poi since there's not much of a "start stop" feel as much as a constant change. I'd call stringing a conventional transmission while poi is more like a CVT (when they're both done right and well).

I am going to state two general criteria that I use to determine if something is a "combo" or not. Keep in mind that either really holds 100% of the time, exactly reflecting how the line between a move and a combo sometimes gets fuzzy.

1 - How much thought the glowsticker put into the "combo". More thought generally makes it more distinctive, original, and complicated than something less thought-out. These characteristics are the ones that I search for when I look for combos. In fact, at times during a video, I can tell when a combo began and ended because I see something very distinctive/original/complicated and then he follows it up maybe by a few repetitive wraps. Then I know his combo ended.

2 - If the technique can go a full circle, or if you can repeat the technique without using anything else. For example, the weave is classified as "move". The weave can repeat itself indefinitely; once we start a weave, we don't need to do anything to keep it going. Same thing with the butterfly, or sun wraps. Any of these poi "moves" can just keep perpetuating themselves. This usually not the case for combos. (Of course, someone can always invent a combo where the hands start in a butterfly and end in a butterfly, thus allowing him to do this combo indefinitely. But then the first criteria, how much thought he put into it, can help us distinguish.)

A combo is a combo when a "move" goes into another "move" eg: Armwraps to arm trace to whatever.

Stringing is nothing more than a combo, "Moves" are foundations, Combos are the end result, Unlike poi, we've never really had to worry about such definitions due to the highly compact feel of stringing due to the situations many of us string in. It's kinda hard to do Anti-spin anything in the middle of a dance floor, thus we move to self made wrapcombos, manipulations, traces, freehand transitions etc.

but really, to keep things simple, "moves" are foundations, "Combos" are the buildings built on those foundations. Without the move, the combo will never be made.

After all, it's kinda hard to do string manips without understanding how strings tangle yeah?

Oo, more levels of structure. Might make things clearer to break up the levels a bit more.
I'm gonna try a linguistic analogy, 'cause I'm a language geek. Say that the whole routine is a paragraph. Then, maybe, combos are like sentences, mini-combos are like phrases, hybrids are like words, and moves are like letters? Or maybe, mini-combos are like clauses, hybrids are phrases, and moves are words. And the individual hand motions are the letters. I like that, 'cause you can take some of the borderline cases and say maybe those are like idiomatic phrases- it's a bunch of different words, but it all means one thing, not necessarily related to the component words at all.I like that analogy. Not sure exactly how to apply it, though.That's my intuitive idea of how it should work- if you can keep doing it continuously, it's a move. But that obviously has fuzzy edges, as you say; with that intuitive definition alone, you could take a whole 3-minute routine that happens to begin and end with the same thing and call it one move, which just doesn't make any freakin' sense. The next bit of intuition is that a move ought to be fairly short, so if it's too long, it's probably a combo- but something like, say, a 16 beat fountain can take a really long time. Which makes me think that the categories do, in fact, overlap.

Oo, insight- perhaps it has something to do with how necessary each bit of motion is to the whole pattern. For example, if you're doing a weave, you can't just stop moving one arm in the middle and keep the other one going. At best, it completely changes the look and you're obviously doing something different; at worst, your strings tangle and you're actually incapable of proceeding with the performance. But with a combo, take out one of the components, and it'll be different, but it still works, and you can probably see the connection between the original and the modification.

I can still think of edge cases, and examples where that doesn't really work, but does it at least not sound crazy?