Well, lets get into it! Great question, because that's definitely how the word "AdX" is used by many players in the industry. Hilariously/embarrassingly, I worked there and still never really got to the bottom of these questions -- they have a strong "don't ask questions about what isn't broken" ethos there when it comes to terminology.

I posted this link above, which is a google-published doc that's much, much clearer than the usual "Help" pages: https://static.googleusercontent.com/media/www.google.com/en...

  The DoubleClick Ad Exchange is a real-time marketplace to **buy** and sell display advertising space.

Right off the bat, that's an awfully good sign that AdX is the exchange, not the publisher network. This also meshes with the image published by the DoJ[1] showing "DoubleClick for Publishers" as the pub network that you're referring to, and "Google AdExchange" as the omnipresent exchange that people who are neither buying nor selling through google must nonetheless go through if they want to leverage the wider ecosystem. It goes on like this, e.g.:

  ### Who Participates in the Ad Exchange?
  1. The large online publishers (sellers)—websites like portals, entertainment sites and news sites
  2. **Ad networks and agency holding companies** that operate networks (buyers)—companies that connect web sites with advertisers

Of course anyone, Facebook included, can setup their own walled garden for direct ad sales, and AFAIU big fish like NYT and CNN do that already, not to mention the separate search ads ecosystem. But to take part in the wider algorithmic Display Ad sales market, my understanding of the DoJ's complaint is that you're (de facto) mandated to use Google's exchange.

But, again; I struggled to understand these distinctions even with access to internal explainers, and the doc I linked is at least somewhat OOD (it mentions AdWords, which was retired in 2018[2]). So I could easily just be somewhat slow and mistaken on this complex issue :)

[1] https://www.justice.gov/d9/styles/d09/public/press-releases/...

[2] https://en.wikipedia.org/wiki/Google_Ads