I guess it may depend if it is on company time and purposes or your own.
I know that driving a car to work is not considered work but I think to get out of a truck then run around in a car throughout your break then get back into the truck may be frowned on as you are not 'resting'
Having lived through a pandemic I now understand all the painting of fat people on couches!
There was something in the old log books about "driving any other vehicle...in connection with a journey in a heavy vehicle" being counted as work time. To my mind that could include driving a car from home to the base, but the RTA confirmed that it didn't. Considering some drivers live up tp 2 hours drive away, that must eat into their effective "rest" time., even if it is not "driving".
As for "rest", many people would probably work harder on their days off than they do behind the wheel, so they might not necessarily get any proper rest.