No, the cloud is a term for dynamically provisionable resources, some of which (IaaS, for instance) still require traditional server management.
It's true that the invention of the term, originally for Amazon's Functions-aaS, wasn't particularly distinguishing from lots of existing cloud SaaS categories (classical PaaS, DBaaS, etc.) which are equally free of server management to FaaS services, but the terms has subsequently been broadened in use (AFAICT, Google Cloud Platform was the main driver here) so that it makes more sense than Amazon's original use did.
Hmm. Your reply has left me even more confused about the nomenclature. Oh well, I guess it doesn't matter if I actually understand what these names mean or not.
