The original Wonder Boy is what Adventure Island was based on. I haven't played the later Wonder Boy games, but it's my understanding that they're pretty different. For one thing, they have RPG elements and non-linearity.
@New Forms The Wonder Boy series is generally very highly-praised. Wonder Boy III: The Dragon's Trap I've seen described by multiple people who'ved played it as one of the best 8-bit games ever made; even rivaling Super Mario Bros. 3 for that title. I have yet to play any of the series (aside from the first game, which is unlike the others), but it's one I plan on going through someday, when I have the time.
From what I understand, the Wonder Boy sequels aren't like the first game at all. Where the first game was like the first Adventure Island, but much better, the other games are Metroid-like in design and include RPG elements.
There's two separate but intertwining series; Wonder Boy and Monster World. Thus you get stuff like Wonder Boy 5: Monster World 3 or some silly thing like that. Finally Monster World IV came out, as the first game in that series that's not also a "Wonder Boy" game (probably because the main character is a girl), and that is one of the two that will soon finally have an official English release, thanks to this coming VC release