My info on this may be a bit dated now, but my understanding is as follows:
For CPDLC, there are two supported connections, these being the Current Data Authority (CDA) and the Next Data Authority (NDA). By only having these two connections for CPDLC, it ensures that there cannot be conflicting instructions issued to an aircraft from different locations, as in, only one Controller can issue control instructions. The NDA is so the aircraft knows that when the CDA disconnects, it has an established NDA to switch to and then accept control instructions only from that next unit.
Sometimes the switch doesn't flow smoothly for reasons, then it's SELCAL on HF to :"Disconnect CPDLC and log on to XXXX"
For ADS-C, there are several simultaneous connections supported, examples may be: Previous ATC unit, Current ATC unit, Next ATC unit, Company Operator, Airframe and Engine Monitoring etc. Current ATC unit is obvious. Next ATC unit ensures seamless connection and associated separation standards can be maintained across the border (some standards are ADS-C Reliant). Previous ATC unit for similar reasons, also, depending on the airspace, changes to track/level may need to be agreed upon by coordination between the current unit and the previous unit until a certain distance/time after the border crossing (10 minutes/15 minutes/50NM...).
TLDR: CPDLC only allows control instructions from one ATC unit. ADS-C, many units may have an interest.