IIRC, you have 3 main types of shot. Cannon,chain, and grapeshot. Save cannonballs, which do ship damage, when your a bit out of your league...say a barque confronted by a Ship of the Line (actually, in that example, run). It will knock out cannon, which is handy. A couple shots can sometimes help when you are facing a tough, but not overwhelming opponent (to knock out cannons).
If you intend to plunder, you usually want to use chainshot and grapeshot. Chainshot damages the sails and rigging (so don't overdue it if you want to keep the ship or it will be slow sailing), grapeshot kills crew.
Caveat-this is from my memory of the PC version, last played probably in 2006.