Disclaimer: Former Red Hat employee working on OpenShift
Correct, OpenShift has been around longer than k8s. Red Hat identified that K8s was a remarkable platform for platforms, and rewrote OpenShift on top it.
OpenShift is good on clouds, but the real shine is on-prem. For anybody with on-prem hardware, OpenShift gives you an abstraction that you can use to make it indistinguishable to your users where something is running. This means you can go cloud when scaling quickly is required, and you can build the foundation on-prem where you save a ton of money. The apps won't have to change at all (as long as they're using the OpenShift abstractions rather than say an EBS storage operator that requires AWS).
Considering K8s (and/or OpenShift) only in a cloud context, is a huge error that will lead one to completely miss the "why" behind why they're so important.
Openshift started as a paas that ran on... AWS.