I think you may have some of the terminology confused, but despite that my guess would be that you are pretty much correct.
First, ADS-B is not used in the oceanic environment; it's something completely different.
The two types of ACARS-based communications with ATC are CPDLC and ADS-C.
CPLDC is the one where you can send manual position reports using the send button, along with other control messages e.g. requesting a different level.
ADS-C you as the pilot pretty much have no control over, ATC set the contract reporting rate and position reports are sent automatically.
I'm not familiar with either of the FIRs in question but it sounds like Oakland use CPDLC and ADS-C but maybe Tokyo only use CPDLC.