Fun Fact: An animated Castlevania film inspired by Dracula's Curse has been on-and-off in production since 2005.
Castlevania III returned to series roots and was a more traditional platformer. In many ways, Dracula's Curse felt like the proper sequel to the original Castlevania, with Simon's Quest being more of an experiment in-between the two games.
Castlevania III was a prequel. Players took the role of Trevor Belmont, an ancestor of the hero of Castlevania, Simon Belmont, and set out to once again infiltrate Count Dracula's castle and destroy him. This third game in the series added some important twists to the formula, like branching paths on the main campaign map which provided a ton of replay value to the game through multiple endings determined by those pathing decisions.
Players were also not limited only to Trevor Belmont as a playable character. Depending on which path they took, there were three different supporting characters to meet. Grant was a pirate ghost first presented as an enemy for the player to defeat, who could climb on walls and change direction in the air. Alucard was the half-vampire son of Dracula who could shoot fireballs and turn into a bat. Sypha was another vampire hunter who used spells to fight the enemy. Once the player chose an ally, they could switch between Trevor and their ally at any time by pressing the select button. Both characters shared the same health meter.
Castlevania III: Dracula's Curse was an improvement across the board for the Castlevania series. The visuals were more colorful and varied, the mechanics more complex, and the music was simply amazing.