My understanding: Like you mentioned the main difference is that digital cash is an abstract type. With our current cash we can very easily convert to/from an int currency to physical cash.
With digital cash it might be more difficult, potentially intrusive or costly to convert to physical assets (look at crypto). If I take $20 out of my bank account and buy donuts, it's going to be very hard to the government to trace that. That will not be the case for digital cash. They will know the exact wallet that came from.
I also believe the need for the Fed for a CBDC is forced onto them because of the inevitability of a negative interest rate on savings accounts (which carries negative consequences). Indirectly, CBDC solves that for them. This person explains it practically: youtu.be/UP0e9MGjyD4
With digital cash it might be more difficult, potentially intrusive or costly to convert to physical assets (look at crypto). If I take $20 out of my bank account and buy donuts, it's going to be very hard to the government to trace that. That will not be the case for digital cash. They will know the exact wallet that came from.
I also believe the need for the Fed for a CBDC is forced onto them because of the inevitability of a negative interest rate on savings accounts (which carries negative consequences). Indirectly, CBDC solves that for them. This person explains it practically: youtu.be/UP0e9MGjyD4