DC Comics ruler of hell?

I'm really confused who the rulers of hell are in DC comics. I bought Sandman v1 recently and the rulers of hell were lucifer morningstar, beezlebub and azazel. But in Demon Knights the ruler is Lucifer? I'm confused about the difference between Lucifer and Lucifer Morningstar, are they the same? Also in Teen Ttitans i thought Trigon and Neron were the rulers, im seriously confused

@tahmidk: The DCU and the Vertigo Universe are different, or that was the case until the DCnU

In christian mythology, Lucifer is the ruler of hell and it is simpler to just follow Christian mythology. Dc does have other less popular citizens of hell like Lord Satanus, Neron, etc.

Isn't it dependent on which religion/mythology you're talking about? Because the Greek myths are real in DC, which has Hades as the lord of the Underworld, which is the Greek Hell... at least I think that's how it works.

@tahmidk: In the Vertigo universe (I'm putting this in spoilers because you haven't finished Sandman/Lucifer yet) the rulers of Hell were:

In the DCU, it was Neron, then Satanus, then Satanus' sister whose name I'm blanking on, though to be honest everyone ignored the whole Satanus/Satanus' sister thing.

In the New 52, it's a version of Lucifer NOT to be confused with the Vertigo version.

The female demon was Blaze.