Both are digital, both can be transferred digital, and both are denominated in the same currency. A CBDC is "a direct liability of the central bank, rather than of private banks or coin issuers", but in an age where currency is not backed by anything I don't understand what it actually means.
Furthermore, it seems that private banks will still be the interface for CBDCs, which means you don't hold them with the central bank either. So what is the real difference from our current system? How would the introduction of a CBDC change anything?