URG!!!
I just posted something for you but I pressed back by accident...
Alright I'm just going to give the page to you.
http://forums.legendsalliance.com/index.php?showtopic=14202&st=960&p=406394&#entry406394
ALOT of quotes from twinrova implying the summon creatures from darkness etc. Look...
Because as Smertios pointed out, Yami no maou is a specific title, only given to the holder of the Trident of Darkness. There isn't a game where Ganon is called Yami no maou in which he doesn't have the Trident.
Also titles are important for OoX because Ganon being revived as Daimaou means he...
He's a Mau when Ganondorf, and then in the final figt when he becomes Ganon he becomes a Daimaou.
Because King of Darkness is ONLY a title given to someone with the Trident. In no game where Ganon doesn't have the Trident is he called Yami no maou.
I'm only going to respond to the OP here:
Demon King = Daimaou = Big Demon King.
In other words, someone who's Daimaou only has to be a Demon. HOWEVER, Yami no maou is a special title only given to Ganon when he obtains the Trident or Darkness.