The morag tong kill in the name of Mephala, the dark brotherhood in the name of sithisĀ
http://www.uesp.net/wiki/Lore:Morag_Tong
And the dark brother hood had religious differences with the morag tong, and broke off, although this isn't 100% confirmed
There is no one answer, by some accounts the Night Mother is Mephala, but this theory is suspect to me because the Night Mother's body was buried in Bravil, and later carted about by Cicero. I'm pretty sure a Daedra Lord wouldn't have a mortal corpse.
The best theory in my estimation is that Night Mother is an immortal spirit of someone who was once mortal, most likely the individual that Matt mentioned, who then became the bride of Sithis. Sithis presumably granted her spirit the divine power needed to hear the prayers of people needing assassinations and relay that information the the Brotherhood.
The Dark Brotherhood basically worships death itself (Sithis) whereas the Morag Tong answer directly to a Daedra Lord. Sithis simply enjoys death, the Night Mother is his messenger so to speak. Mephala on the other hand is a bit more specific in her goals and intentions and has fun causing trouble for mortals.
It's been hinted at a few times, but there's very little soild evidence. The one thing that gets me, is that, in Daggerfall, the Dark Brotherhood worships Mephala. Of course, the real world answer is that the concept of the Night Mother and the Black Hand hadn't been invented back then.