BEA's Peter Laird just posted a great overview of Cloud Computing, SaaS, and Platform-as-a-Service PaaS for those who are still struggling to figure it out (and really who isn't?)
As always, the definitions are vague, yet arguable but I think they do a good job in establishing what we are talking about.
Cloud computing refers to the virtualization of the data center, such that server machines are not thought of individually but as just a commodity in a greater collection of server machines. Cloud computing solutions in general strive to eliminate the need for an application deployer to be aware of the actual physical machines that are used to host the application. Some have called this idea "hardware as a service".
An application that is delivered through the SaaS model typically is done so:
-Over the internet
-Remotely by a third party, with little/no opportunity to bring that application in-house
-With a usage-based pricing model
When a vendor offers a Platform as a Service, they are offering an integrated platform to build, test, and deploy custom applications.