Colin Booth:
The distinction is specifically thus: ./up is what fires when the service is brought up, ./down is what fires when the service is brought down, ./run is what fires when a non-running service is supposed to be running, and ./finish is when a running service stops. Just because oneshots don't support run or finish, or that longruns don't support up or down, doesn't mean that the separation of duties is any different.
Just for comparison, since you are hunting for names: In nosh, which re-uses the daemontools-encore state model: ./start is what runs in the starting state when the service is started from the stopped state; ./stop is what runs in the stopping state when the service is stopped from the running state; ./run is what runs in the running state; and ./restart is what runs in the failed state, before either going back to running or going through stopping to stopped. systemd's "Type=oneshot" translates to a service with its meat in ./start with ./run either executing pause or true. (See http://homepage.ntlworld.com./jonathan.deboynepollard/FGA/unix-daemon-readiness-protocol-problems.html for the readiness protocol that this is replicating.)
