After a quick bit of digging, I discovered that PaaS seems to be a term coined by Salesforce, to describe a platform for building software as a service.
It's what I used to call framework as a service. I think Nick is right, there really are too many aaS's. I've tried to express this in Venn form in the following diagram.
In reality, these various forms of "as a Service" simply represent different aspects of the commoditisation of the software stack from a product based economy to a service one (see figure 2). Don't get bogged down in the different acronyms being used; the underlying concepts behind this change are the important thing to understand.
Video of OSCON talk - Commoditisation of IT (approx 15 minutes)