Looks to me that Apache Mesos is a distributed systems kernel, and Mesosphere is something Linux distribution based on Apache Mesos.
For example, its like Linux Kernel(Apache Mesos) and Ubuntu(Mesosphere).
Am I right about this?
and DCOS is a free edition of Mesosphere, like RedHat vs RedHat Enterprise?
Let me try ;-)
Apache Mesos - OpenSource Cluster Resource Manager, Kernel of DC/OS
Mesosphere - Company contributing to both Apache Mesos and DC/OS
DC/OS - OpenSource Distribution around Apache Mesos including UI, networking, and many other pieces. Mesosphere also offers an Enterprise Edition of DC/OS with support and some advanced features.
Hope this helped!