Most bows have only piercing damage, which goes through armor better than cutting and blunt, and the rest do additional elemental damage, which is not affected by armor.
As a bit of clarification to this - if a bow has armor penetration, it will list "ignores X% of enemy defense" or something like that in the tooltip when you hover your cursor over the bow in your inventory. Also, piercing does not (as far as I know) go through armor any better than cutting or blunt, but you might see less defense against piercing attacks than against cutting or blunt attacks. For reference, chain armors of any type have a base amount of defense, which is used against both blunt and piercing damage, and then have a defense bonus against cutting damage (which doubles the defense, making cutting weapons much less appealing against chain armors), while all plate armors have the same amount of defense against cutting and piercing damage and a defense bonus (again doubling their defense) against blunt damage.
If you select a unit and highlight the defense score, you'll see a tooltip pop up with a breakdown of the unit's defense rating - first the base defense, then a column labelled cutting (the total defense against cutting attacks), and last a column labelled blunt (the total defense against blunt attacks). There are a few units in the game that have particularly high or particularly low defense scores against certain types of attacks, and it can help to check their defenses before building a bunch of units that can barely scratch whatever you were trying to fight.
To the best of my knowledge, the base defense score is the same as the piercing defense. I'm not aware of any abilities or equipment that increases defense against piercing damage.
