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.
Both OpenShift and OKD are open source. The subscription requirements of OpenShift, RHEL, and other Red Hat products don't interfere with their open source status because they a subscription is actually a support contract. That support contract imposes terms of use that are independent of the open source license of the upstream software.
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.
