Wonder Boy III is a platformer/shooter hybrid. It was released on both Mega Drive and PC Engine. There is no Wonder Boy 2.
Contrary to popular belief, the Monster World games are not related to Wonder Boy OR Adventure Island. They share some similiarities design-wise (level design and graphics) and they were developed by the same company (Westone) but that is about it. Some (idiot) decided to name all the games Wonder Boy when they got released outside of Japan. Just because, you know, cause some confusion.
These are all the Monster World games and what they got released as outside of Japan:
Monster WorldSega Master System - Wonder Boy in Monster Land
PC Engine - Bikkuriman World (never released outside of Japan)
(I believe this game got released on various other crap systems not worth mentioning.)Monster World IISega Master System - Wonder Boy: The Dragon's Trap
PC Engine - Dragon's Curse
Monster World IIISega Master System - Wonder Boy in Monster World
Sega Mega Drive - Wonder Boy in Monster World
PC Engine - The Dynastic Hero
Monster World IVSega Mega Drive - Monster World IV (never released outside of Japan)
Monster World III and IV (MD versions, of course) got released on seperate CD-ROMs for Windows a few years ago. These are not remakes or anything but just emulated versions of the games. They got delivered in regular jewel cases. Westone went bankrupt a couple of years ago. Big surprise.