The official definition of Platform as a Service (PaaS) from the National Institute of Standards and Technology (NIST) states the following:
"Cloud Platform as a Service (PaaS): The capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or -acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations."
This definition focuses on the consumer view of PaaS in which the provider dictates everything underneath the application layer, including the underlying platform and infrastructure.
What is notable about the definition is what it does not include. There is no statement about the details of multi-tenancy in the application, or how the application does (or does not) make use of elastic resources. There is also no requirement that the provider supply special, cloud-only tools to build applications.
In fact, the notion of an application lifecycle is not mentioned, allowing the possibility that no development or operational tools are provided at all. Finally, there is no mention of the type of cloud infrastructure, whether it is private or public, and no mention of the details of the compute infrastructure that is used to power the cloud.
To learn more about IBM point of view of Platform as a Service download this whitepaper below.