It's not the same. Strangely the docker-swarm tutorial doesn't mention swarm mode. I wasn't able to follow it successfully with Docker 1.12. That was when I realized docker-swarm != swarm mode, so I tried the swarm mode tutorial instead, and it worked as expected.
Maybe docker-swarm is not supported anymore with 1.12? It was all pretty confusing.
Originally, there was the stand alone version of docker swarm, invoked using "docker-swarm". This was more difficult to set up than version 1.12's new swarm mode, invoked using "docker swarm", which does almost the same thing, but more succinctly. Presumably, they chose the same name because they serve the same purpose and, if the latter is set to replace the former, why come up with a new name for basically the same concept?
Why would one use docker swarm[1] vs just docker swarm mode.
1.https://github.com/docker/swarm