OpenShift is Red Hat's commercial container platform built on Kubernetes. It includes a lot of additional components that are useful in the everyday operations of Kubernetes clusters. You get a container registry, a build tool similar to Jenkins, Prometheus for monitoring, Istio for service mesh, and Jaeger for tracing. It is not fully compatible with Kubernetes so it shouldn't be thought of as a drop-in replacement.
It is built on top of existing Red Hat technology such as CoreOS and Red Hat Enterprise Linux. You can use it on-premises, within Red Hat Cloud, on one of the supported public cloud providers (including AWS, GCP, IBM, and Microsoft Azure), or as a hybrid cloud.
There is also an open source community-supported project called OKD, which forms the basis of Red Hat's OpenShift. If you do not require commercial support and other benefits of OpenShift, you may still use OKD for your Kubernetes workflow.