Multiple Pods for multiple clients on a single Kubernetes Instance
I'm trying to wrap my head around how/if Kubernetes manages multiple Pods in terms of a clustered client model. Based on this documentation Multi-container it sounds as though Kubernetes is only concerned with the health of a pod and the containers within it. This means that a single Kubernetes instance could manage multiple client's pods, which contain containers running that client's applications, microservices etc. 
Is this correct?
Please see my diagram for a clearer idea of what I'm asking.
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The diagram has the right idea, but not quite the right terminology.
The diagram would be more accurate if the "Pod" label was replaced with "Namespace", and the "Container" label was replaced with "Pod".
A single Kubernetes cluster is intended to be able to support multi-tenancy, where the workloads of individual clients can run with proper security, resource allocation, isolation, and other important tenancy management attributes.
The unit of tenancy, however, is a namespace- a logical layer of abstraction in which are deployed workloads, usually for an individual client- not a pod, and the unit of replication for workload processing is the pod (comprising one or more containers), not an individual container.