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.
Video of OSCON talk - Commoditisation of IT (approx 15 minutes)