You can open Docker Desktop on Mac using:-
open -a Docker
The Mac equivalent to systemctl or service is launchctl. But Docker Desktop is, presumably deliberately, packaged both on Mac and Windows as an application, not a service.
For shutdown, this:-
pkill -SIGHUP -f /Applications/Docker.app 'docker serve'
seems to work about as well as Quitting Docker from the GUI. By which I mean (a) when you restart Docker again it starts up with no complaints and (b) however I quit Docker Desktop, I still have a docker networking daemon left running.