There is lots of confusion with CPDLC / ADS-C / ADS-B / DCL. A lot of the blame goes to the avionics manufacturers, and a lot to the training centers. I can only speak to the Gulfstream Primus Epic cockpit, so here comes my two cents:

DCL - Domestically, and ONLY domestically, DCL is tied to the FANS system (CPDLC). You log onto the airport (if the DAT 1FANS2PDC is properly filed in item 18) and the tower automatically sends you the clearance at the Proposed Time minus 30 minutes. You remain logged on till takeoff + 5 or 10 minutes. We got a full route re-clearance while holding number 1 at HPN via DCL, accepted it, loaded it with two button pushes, and were good to go in less than a minute.

In Europe, you get the DCL from the DATALINK - ATS - DCL button sequence, not from FANS. It comes from the ACARS system from which you get DATIS and PDC's, there's no CPDLC involved. Right now there are very few airports using it.

For oceanic clearances, there's no FANS / CPDLC involved either. You may be loggged on to an active center, but you get your clearance via DATALINK - ATS - OCANIC CLX, NOT from CPDLC. It's called an RCL (request clearance) and you ack it by CLA (clearance acknowlegment).

For CPDLC, the ACT ATC center should automatically transition very close to the center boundary. There can only be one active center. The ADS-C "contracts" don't transition, the various centers log on to your jet and there can be multiple centers logged on requesting multiple bits of information from you - your route, when your jet should tattle on you (300' off altitude, 15 miles off course), wx info etc.

ADS-B is another moster entirely and comes from your transponder.

That's it for now, happy Datalinking and fly safe!