There are technically three types of the game Pirates of the Caribbean: Dead Man's Chest. Each one is different is the way they are played and the presentation.
The psp version of Pirates is a 3D hack'n'slash game. You run around and defeat the enemies before they defeat you. You have essentially two different attacks, which, when used in a specific order, will defeat different enemies. You can also use alternative weapons, which include bottles and throwing knives, which immediately One-Hit-KO's the enemy.
The GBA version of Pirates is an open-ended 2D platformer ARPG. While following the events of the movie Jack will sail around the islands of the Caribbean. Each island has a store and several 2D levels filled with enemies to pass through. By learning rumors Jack can find treasures in these levels. Some treasures level up Jack or the Black Pearl's stats, while others are needed to convince new shipmates to join Jack's crew.
Jack always has his cutlass with him in fights, and he can learn a small number of combos over the course of the game. On the open sea the Black Pearl can get into ship-to-ship fights with other pirates or the royal navy. In ship fights both ships try to maneuver into position to fire their cannons, but the crew will need time to reload after each salvo. Both Jack and the Black Pearl can use limited ammunition weapons, like throwing knives and burning oil for Jack, or ballast and chained shots for the Pearl.
After a sea battle opponent is sufficiently weakened it can either be boarded, switching to a side scrolling level where Jack loots its holds while fighting the crew, or just destroyed outright. The Pearl can be upgraded with new guns, masts, and hulls found on boats, or purchased in stores.