Installing the current OKD is basically the same as installing OpenShift 4, which means you cannot install it on RHEL alone. You require at minimum three Red Hat CoreOS nodes (I guess it is Fedora CoreOS for OKD) for the control plane. It is possible to create these as VMs using virt-manager and virtctl from RHEL, Fedora, and other OSes.
A better way of referring to the differente between OKD and OpenShift, or between CoreOS Stream and RHEL, is stating that the first couple (OKD and CoreOS Stream) are community supported software, and the second couple (OpenShift and RHEL) are comercially supported software.
That said, yes OKD is the community version of OpenShift and there is no difference in features, command syntax, Kubernetes resources, and compatibility with container images and Kubernetes operators.