Payments
A stablecoin, a tokenised deposit, and a CBDC are different debts.
One may be a claim on a private issuer's reserves. One is a bank deposit in a new wrapper. One would be a central-bank liability, if that bank has actually issued it.
Do not sort them by the logo
A stablecoin's peg is either redeemable reserves, over-collateral, or a mechanism that leans on another token of the same system. Terra showed the third kind can fail. A tokenised deposit keeps the bank's credit risk. A CBDC is not a white paper and not a pilot. It is an issuance, or it is not.
Settlement
Sending the token is not the same as discharging the obligation in law. Say which moment you mean. A pause by an issuer, a chain, or a bank is an operating fact, not a footnote.