I think OP is quite aware of the distinction, yet I would also argue that 'serverless' doesn't apply to having to manage a Kubernetes cluster (on servers.) If you are only exposed at the services level - whether they are provided directly by your cloud provider, and whether or not those FaaS & buckets are implemented with k8s hidden from you, then you can use 'serverless', but not if part of the requirement is to manage that k8s stack yourself - and that includes provisioning so-called FaaS on the cluster. "Serverless" it decidedly is not.