Difference between openshift kubernetes version and googles kubernetes

OpenShift is a PaaS layer on top of Kubernetes, so there really isn't a difference in the Kubernetes part of the stack. However, OpenShift embeds many Kubernetes (and Etcd) binaries in their distribution, so it isn't always 100% obvious that Kubernetes is somewhere underneath because you don't interact the the stock server-side Kubernetes components in the same way. OpenShift also layers on additional/different functionality like more types of authorization/authentication, watching container registries for changes (imageStreams), container builds, a different UI, etc. (Check out the docs for a more complete overview).

One downside of this embedded approach, is that installing OpenShift on top of an existing Kubernetes cluster is more difficult and less documented than the embedded approach that RedHat has to support for their customers. It looks like there is some work lined up to address that. Right now, there is an example of doing this OpenShift-on-top-of-stock-Kubernetes in the Kubernetes repo, but my experience with this is that this approach is more exploratory (and somewhat out of date when I last tried it), than anything you'd use for production.