What's the relation between the King in Yellow (40k) and the King in Yellow (Robert W Chambers)

From my understanding the King in Yellow 40k is Constantine Valdor, the custode. But is there any relation between him and the King in Yellow from the Book.

From my understanding the book has several separate stories about a Play called "The King in Yellow" where its readers are driven to insanity and then Death if they read it. The King in Yellow is also the name of a character, who doesn't really show up. He is presented as a sort of outer god and he rules of a strange city with a lake and twin moons and when the characters from the separate stories die (if they do) they seem to go there. It reminds me of another 40k story I heard that I cannot name about a man who dies and travels to a world of ash and dust with a crippled man (suspected to be the emperor) who sits upon a chair, and then I think he dies? idk.

So what's the relationship between the two, and also what's that story about a world of ash and dust?