[Ninja Pirate]

Ok quick rundown of ships

Sloops = fast with good manoeuvring
Galleon = fat and slow with big cargo holds
Frigate = well armored lots of guns

You can upgrade broadside with skill points from sailing skill and you buy different cannon ammo from gunsmith.

Edit:Those ships that don't sink are probably flagships you need to board them and you can only do that if you deal the final blow.