Ammo is the collective name for projectiles that can be fired from ranged weapons, and can be put into the four ammo slots that are available in your inventory. Arrows and bullets will be automatically put there once you pick them up, unless the slots are full.
Ammo includes (but is not limited to): Wooden Arrows, Flaming Arrows, Unholy Arrows, Hellfire Arrows, Jester's Arrows, Holy Arrows, Cursed Arrows, Musket Balls, Meteor Shot, Silver Bullets, Cursed Bullets, Crystal Bullets, Fallen Stars (for the Star Cannon ) and Gel (for the Flamethrower). All of these can be stacked up until 250 (with the exception of fallen stars, which can only be stacked to 100).
Arrows are projectiles that can be fired from a Bow or Crossbow (Repeater). They have a variable chance of remaining intact upon hitting a block or monster, and can then be picked up again (However, 2/3 of retrieved Cursed or Flaming arrows will be normal arrows). They travel in an arc at a moderate speed, and have many variations (some shown to the right).
Bullets are projectiles that can be fired from a gun. They can't be picked up again, after being shot, like arrows, but travel in a straight line towards the target, and travel a lot faster. They also have a few variations. (2 shown to the right) They can be shot from almost any Gun.
Fallen Stars, Seeds, Sand, Gel and anything else that isn't a bullet or an arrow, but that can be put into an ammo slot, falls under this category. These are items that can often be used in one or more other ways