no. there is no clear distinction like that with coreOS.
Its just one of the distributions that try to be a ... docker hypervisor for lack of a better term.
It tries to be a tiny distribution for the sole purpose of letting you use a docker daemon.
a direct competitor would be RancherOS
/edit: furthermore, the kubernetes docker daemon is (afaik) a fork from the original docker and predates docker swarm by a long time. It was the only way to really scale with docker back then.
Docker Swarm seems to be a viable alternative at this point, however. And honestly, its way easier to use from my experience.