The only time I have heard of dry (and wet) ammunition is in tanks like the old Sherman tank. The Shermans had a reputation for catching fire easily in battle, so much so that they were given the nickname “Ronsons”, which was the name of a cigarette lighter at the time whose slogan was “lights the first time, every time”.
Initially, the ammo in the turret was stored in “dry” racks. Nearby fuel tanks may have led to the Sherman’s “Ronson” reputation. Anyway, if the ammo racks were hit, they could easily catch fire, which was very bad news to anyone inside the tank. To reduce the chance of ammunition fires, the ammo was moved to “wet” tanks below the gunner. The ammo stored in these tanks was surrounded by a mixture of water and ethylene glycol and probably some other stuff that I’m not remembering (it wasn’t just water).
In that context, wet ammunition was the stuff in the wet tanks under the gunner and dry ammunition was the stuff in racks up next to the gunner in the turret.
That doesn’t really fit with the context of the OP, but in the OP’s case it may refer to ammunition that is just stored in racks somewhere.