The alternate English title is "I'm Luffy! The Man Who's Gonna Be King of the Pirates."
In the manga, the setting was on an island, but in the anime, it was on the Lady Mary.
In the manga, Alvida and her crew seriously discuss the possibility that Koby had hired Roronoa Zoro to attack them. This is simplified in the anime, with Alvida simply mistaking Luffy as a bounty hunter.
A scene is added that shows Luffy and Koby in the cellar where Luffy is eating apples.
In the manga, Koby shows Luffy a boat that he built in 2 years to escape from Alvida. This is not shown in the anime.