right… there are three commands here
docker run - start container for 1st time
docker stop container… stops, but does not cause container to exit
docker start container, which resumes a container that had docker STOP issued on it
and there is docker kill which terminates a container… the container is not restartable.
and if it was initially started (doker run) with --rm, then the container instance is destroyed (auto docker rm) on exit.
docker status will show you the container current state. (running, stopped, exited)