My take on it was that when Dracula died, his powers were fragmented. His soul wandered the void for a while before reincarnating into Soma. That being said, Soma got the largest chunk of what was once Dracula's power over chaos. Those born on the same day that Dracula was defeated all received small traces of Drac's power, that could be augmented and used at any time in the future. Hence, the Dark Lord Candidates.
The Dark Lord Candidates all have traces of Dracula's power as well, though not nearly as much as Soma since he has Dracula's full soul, and thus he has the largest bid over the powers of Chaos. If Soma were to be killed, then whomever had the next largest amount of Dracula's powers within them would in theory be the next in line to control the powers of Chaos. Given that every Dark Lord Candidate has roughly the same amount of Dracula's power within them (to begin with at least), then any of them could be the next in line for that bid on Chaos.
This would explain how Graham was able to wield the Castle's powers after a certain amount of time of being exposed inside it - it recognized the faint amounts of Dracula's power within him, and simply augmented them. He fed off the Castle, in a sense. However, Soma didn't necessarily need the Castle's influence to access his powers, hence he was the stronger of the two. Both Dario and Dimitri had powers to begin with, but they were augmented by the demons of chaos that Celia summoned for them....instead of feeding off Castlevania like Graham.
So basically, Soma is Dracula and the Dark Lord, but someone else could become the Dark Lord if Soma were to be killed and the powers of chaos moved onto the next person who could access them. However, only Soma is Dracula and that can't be changed until he dies and his soul is reincarnated again.
Savvy?