Close, but once the handshake is made the car determines most of the process. If it decides to draw a lower current, it doesn’t tell the wall box, it just does it.
In the initial handshake, the wall box can tell the car to only draw, say 8 amps, and car will comply. It’s not possible for the wall box to increase or decrease the charging rate once it starts (which is a shame).
The wall box contains a contactor and it can stop the charge at anytime if it sees an error or problem. Some wall boxes have temperature sensors in the charging plug.
I have a degree in Electronic Engineering, I do understand the process, I studied it with a view to making my own wall box.
All control signals are analogue and not digital.