The game was remade for the Gameboy Color, and including a new translation that is closer to the original Japanese storyline, and includes new locations, including a new dungeon and a bonus board-style minigame found in several locations.
What wasn't included in the original North American release of Dragon Warrior III for the NES was restored for the Game Boy Color release, therefore giving it a Teen rating.
The version originally released for Nintendo was censored for content:
A tavern became an eatery.
Religion was toned town.
The dead were not as 'disturbing' when traveling behind you.
There were no "puff-puffs." ("Puff-puffs" have become widely debated on the internet and between fans as to what it is. Some think that it is a reference to oral sex, while others see it as a man receiving a massage with a woman's genitals or breasts. No one really knows...)
The version for Game Boy Color restores this content, making it a remake of the original game.