Bow
From Dwarf Fortress Wiki
A bow works the same way as a crossbow, except that is uses arrows instead of bolts. Dwarves cannot equip bows (stubby fingers), and the interface is such that they still cannot be wielded in Fortress Mode at all, even with modding. They can still be used in weapon traps, although you can't make arrows and so will be dependent on merchants and spoils of war to supply trap reloads.
When firing arrows it uses the bowman skill. When attacking with melee, it uses the swordsman skill, although it's a bludgeoning attack.
Arrows
An arrow is just like a bolt but for bows. Dwarves can't handle bows, so they don't need arrows. But in adventure mode, humans and elves can use bows, so they will need arrows if they choose to use one.
Arrows can also be thrown in adventure mode for about the same results, except that it uses the thrower skill.
