There's an acronym called PAAS, which is Platform as a Service, and it's analogous to SAAS (Software as a service) and IAAS (infrastructure as a service). The idea is that an application platform exists in the cloud and you essentially upload your code, allowing the provisioning, scaling, and other details to be handled by the platform is interesting.
I think that statement is slightly off. PaaS is not directly analogous to SaaS and IAAS. The subtle differences are demonstrated if you think of each of them in terms of layers.
In order from the most control (for the client) to least control:
Co-location (Facility as a Service?): You get a cage with power and internet, what you put in there is your concern.
HaaS/IaaS: The client leases the use of hardware (usually virtualized). Customer is responsible for everything above the VM layer.
PaaS: The provider handles the hardware, and OS configuration, and some platform on top of it (SalesForce, Azure SQL, etc). The customer uploads code or data that is specially formatted to run on that platform and has no OS level control.
SaaS (formerly ASP): Leased applications. The customer may be responsible for some configuration options in the app, but essentially is outsourcing all of the hardware and software issues to the cloud provider.
Examples of each
HaaS/Iaas: Amazon EC2
PaaS: Microsoft Azure
SaaS: Google Docs, FaceBook, etc.