Review: Dragon Quest VIII
Yes, Dragon Quest == Dragon Warrior.
The reason the series was known as Dragon Warrior in North America is because someone other than Enix, the original maker of Dragon Quest, did not own the rights to the name "Dragon Quest" in the United States; therefore, a different name had to be used. They settled on using "Dragon Warrior" for its North American release. Since then, the trademark on the name "Dragon Quest" has expired, and SquareEnix decided to use the original title from now on.