Port Royale 2 is similar to Port Royal, but some things changed.
The sea battles work differently: in a convoy you must declare a ship as "escort ship" otherwise the convoy won't fight. A convoy can have at max five escort ships, but you will fight with only one at time; while in the battle you can change ship, but the old one will retire. When the battles ends the winner can take all non-escort ships even if escorts flew all. Note also that a ship with no sailors can yet shoot with cannons.
Pirates now have a hiding place and will have more convoys. The pirate can be defeated attacking the hideout and having no convoys out of it. Attacking a pirate hiding place is like attacking a city, with the difference that it can be attacked only from sea and the damaged convoys defending the city will be repaired straight after the attack. However you can take rewards from governors for destroying pirates' convoys.
A city will produce only five types of goods, in relation with the city type. You can have your own cities, though for obtaining all 16 of them you must annex 128 cities.
Trade routes are easier to create and require no effort at all, since the computer alone buys the goods you choose. You can still realize trade routes like in Port Royale, with the option 'manual trade'.