When you use up your ammo*, you're out of ammunition**.
*"ammo" represents the game-mechanical tag with a quantity by it. It will always be italicized.
**"ammunition" represents the fictional concept of having something to fire at the enemy. It will never be italicized.
So, fun fact: nothing about the Volley move or any of the most common ranged weapons you'd want to use with it actually requires you, mechanically, to have any ammo at all. Volley, like most moves in Dungeon World, happens when the fictional circumstances say it happens, not when, say, Fletcher's player says "I Volley at the orc marauders".
What is the fictional circumstance that lets you Volley? Well, it includes having ammunition. So the ammo property which says "it counts as ammunition" is a markedly fiction-facing property. Fletcher's Volleys, even when they don't consume ammo, are not necessarily with exactly one arrow, any more than Shanksworth's Backstab involves exactly one stab or Fightgar's Hack and Slash contains one hack and one slash. Being able to Volley means that, in the story, you have enough ammunition, and as long as you have 1-ammo on you, you can Volley as much as you'd like. (Any amount of sustained, careful fire that would really take up 1-ammo worth of arrows is probably happening at a scale that would be dealt with by a move farther zoomed-out than Volley.)
Tags exist to tell you how equipment plays into the story:
Each piece of equipment will have a number of tags. These will tell you something about how the equipment affects the character using it (like +Armor) or suggest something about the way it is used (like the Range tags). Like everything else in Dungeon World, these guide the fiction you’re creating in play.
So when you drop to a total of 0-ammo, that has story consequences. For story purposes, you no longer have enough ready ammunition for a Volley. That's because the numbers in the ammo tag are also there to mean things in the story, and 0 means 0.
Now, it is still possible to Volley without having 1-ammo! You just have to work out the fiction that goes from "I'm out of ammunition" to "then I find some" to "and keep on firing". If Fletcher's got no arrows left in his inventory but is out on a hilltop where a bunch of friendly archers did that "stab arrows into the ground for easy access" thing, then he has fictional access to enough ammunition to Volley, but can't spend points of ammo for the purposes of moves that care about that. If Shanksworth is fleeing down a cobblestone road it probably isn't too big an ask to find a rock big enough to sling without breaking stride. If Stringfellow has only a bow to stand against a beast swooping out of the night, well, pray to lady luck and search your pockets, bard. And hurry.