Where courtly intrigues, mysteries and horrors shine is in the one thing they have in common.
Secrets.
In courtly intrigue settings, including rampant Casanova - style romantic intrigues where the NPC women are all comely, but challengingly distant, secrets exist as currency. When you have a secret, you have the key to a favour from the person who the secret concerns. Favours can be traded and bartered, and a solid owed you by someone who can grant you a minor favour might be just as powerful as a favour from a more powerful, yet treacherous, patron. And sometimes, the existence of favours and boons is itself a very powerful secret. Knowing that you have the Prince's ear because he owes you his life is one thing; keeping that knowledge secret is something else.
In mysteries, you have to ferret out the secrets based on the clues liberally scattered about the scene. Some of them you stumble upon because you have smart players; others your characters might have to stumble across the hard way, usually at the wrong end of a pitched battle with the bad guy's goons in an alleyway somewhere. But in mysteries, the revelation of secrets is what leads the characters to identify a criminal - moreover, it sometimes happens that the characters need to identify the nature of the crime being committed, that the crime is being committed at all and, most of all, the victim.
And finally horror. Secrets here are not things lightly revealed. They can hurt the character to know, because they are the sorts of things that could keep them up at night. That princess they fought so valiantly to rescue from the vampire king? It turns out that she was the vampire king - or worse, the vampire king's maker, an even older vampire with unthinkable powers. And they let her go ... Or perhaps the revelation that the shapeless Thing that appeared on their doorstep is their old friend, who'd gotten involved with the wrong crowd, a bunch of sorcerers who possess a spell enabling them to swap souls between bodies ... in this case, one of them has swapped his living soul into his old friend's body which is now walking around enjoying his stolen life, and has trapped the soul of the old friend in the sorcerer's dead, rotting body ...
All three have the same spice in the pudding; secrets. It's just the way they're used that differs. And you know the best thing? I can write for all three of those genres. Hint, hint.