So we all know that there is some conspiracy (or conspiracies) going on behind the scenes that has (or have) caused most, if not all, of Harry's major troubles. The first name we get is the Black Council from Harry because mortal practitioners are involved. Then we hear about a Circle in White Night and Changes. In White Night, it is some organization the Malvora and Madrigal Raith are working for, are aware of, and Cowl is the contact for. I find it unclear as to whether the Malvora is "in" the Circle or just an agent of it. In Changes, it is mentioned by the Eebs, but they might just be referring to the Lords of Outer Night.
I think of the Black Council as an organization made up of mortal practitioners, mostly current or former members of the White Council, separate from the Circle. I think of the Circle is an organization with representatives from various supernatural groups with some unknown mutual aims and a lot of backstabbing. The leadership of some supernatural groups are entirely aware of the Circle and part of it. I think the Black Council is one of those groups. Only factions of some groups are aware and represented. The White Council, through the Black Council, would be an example here.
Alternatively, the Black Council and the Circle could be the exact same thing. Either a group of wizards calling themselves the Circle, or a larger supernatural conspiracy that Dresden simply thought was made up of just wizards.
We've got a pretty clear picture of what Nemesis is, if not how it works. It's an Outsider secret agent/sapper/infiltrator.
I think Nemesis influences the Circle but does not control it. It almost certainly controls some of the members of every major supernatural group, including the Circle.
I also think the Circle has only thirteen members for the reasons stated in Storm Front. Additionally, there were thirteen Lords of Outer Night, perhaps for the same reason.
Alternatively, everything is either Nemesis or it's catspaws.
Thoughts?
I think you're onto something here. When I first read about the Black Council, Nemesis, and the Circle - I thought they were the same thing too. But since rereading the Dresden Files, I've come to three possible conclusions:
1. The Black Council is mostly made up of mortal practitioners who've turned their backs on the White Council (warlocks, etc.), but it's just a child compared to the Circle - who controls the Black Council. One or two of the members of the Circle may be infected with Nemesis. Or directly working with the Outsiders. Like Mavra. I think she's most likely a part of the Circle, but not necessarily the Black Council.
2. The Nemesis controls the Circle and the Black Council. The Black Council and the Circle on their own are dangerous enemies to Harry and friends, but the Nemesis made it possible for these two to become a lethal threat to every supernatural being on Earth. I think Nemesis started by creating the Circle, and then worked towards forming the Black Council through the Circle. Someone in the White Council, other than Peabody, is also a traitor.
3. Nicodemus and company planned to steal the five holy relics from Hades' vault because they have their own war against the Outsiders. The Fallen are still angels, and if the Outsiders ever get into the world -- they are a huge threat to the angels' power base. Lea thought the Athame could be used as a weapon against the Outsiders. But I'm guessing it's actually the knife Harry stole. So Nicodemus wanted that specifically but he had to settle for the Holy Grail.
And of course Uriel knew about their plan to steal the relics in advance. As an archangel, he told Harry that he intended to save the souls that were under the influence of the Denarians. But he's been known to work several plans all at once, so I think he also lent his Grace to Michael to ensure that the relics wouldn't fall into the wrong hands once they were stolen. And now that they're out in the world, they can be successfully used against the Outsiders.
So in future books, minions of Nemesis might come gunning for them. Possibly in the form of one of the Circle. Like Mavra. Or another supernatural entity infected with it. At this point, the Black Council can't really risk moving because they risk premature exposure.. so the obvious enemies will come for Harry, while the others work in the background.