Weapons

Ball

 * Basic round solid cannonball. Best for hitting targets at longer ranges to damage the hull and armor of a ship.

Double

 * Two ball rounds fired at the same time. Less range than ball but with higher damage. (No longer in the game)

Chain

 * Two smaller balls connected by a chain. Designed to damage the sails of a ship to reduce it's mobility.

Grape

 * Multiple small round shot designed to kill crew at close range.  Basically turns a cannon into a shotgun.

Types of Cannon:
Naval Artillery in the Age of Sail

Cannon

 * Basic cannons allow versatility in shot types and slightly higher damage output than the long gun.

Long Gun

 * Long guns increase range and projectile speed with the cost of increased reload time.  A flatter trajectory also increases accuracy at higher ranges.

Carronade

 * Carronades are built much lighter than cannons of equivalent caliber.  This means that a much higher caliber carronade can be placed in a smaller cannons position.  However the maximum amount of propellant used is much lower due to lighter construction.  This leads to the ability to fire a larger projectile but at lower velocity and range.  A ship carrying carronades will have to maintain close range to the enemy to apply damage.  This can make carronades an attractive option for lighter ships that can properly dictate range while avoiding enemy broadsides.

Caliber
Age of sail cannons and carronades are rated by caliber which is the weight of their round shot in imperial pounds. This is not to be confused with modern caliber which is categorized by the diameter of projectiles. Increasing caliber of cannon generally increases damage and range at the cost of loading time.