Captains use several kinds of ammunition to load their cannons, depending on situation. There are three basic types of ammo:

Round Shots to damage ship's hull
Dismantling Shots to damage ship's sails and reduce its speed
Anti-personnel Shots to reduce enemy's numbers

In general, if you want to board a ship, you would use Dismantling Shots to slow it down and then Anti-personnel Shots right before the boarding, to kill off the crew. If you are not planning to board a ship, then you can go all the way with Round Shots to sink it.

Ammo for the cannons :

Solid Ammo : Multipurpose, but better than anything against the Hull. Edit

Stone Shot: a round rock. Shatters on impact. Cheap, but not as powerful as Basic Round Shot.

Basic Round Shot: yer basic iron cannonball.

Heavy Round Shot: Heavy round shot has excellent penetrative power against ship hulls, but is far less effective at damaging crew or sails.

Bronze Round Shot: Heavy round shot made from bronze is more effective at penetrating ship hulls than iron shot.

Dismantling Shot : Used primarily against the Sails and Rigging.Edit

Bar Shot: two iron hemispheres joined by a solid bar.

Chain Shot: two iron balls connected by a chain - larger size than either of the above two.

Star Shot: a 10 segment chain formed into a ring. This expands out to cover a huge surface area when fired, but it ends up being somewhat weaker than the above types.

Anti-Personnel Shot : Shotgun theory - extremely effective against crew, less so against other parts of the ship. Edit

Langridge: the poor-man's canister shot. "Langridge" was a fancy name for "shove in lots of nails, gravel, clamshells - whatever" It wasn't terribly effective, but it was easy to come by.

Canister Shot: the standard anti-personnel shot. It was literally a can filled with little iron balls.

Grapeshot: a new ammunition development in the early 18th century, and still (theoretically) restricted to the navy in PotBs.