What are these?
A Platform as a Service (PaaS) is a service where you do not manage the underlying infrastructure. An example of this would be Microsoft's Azure framework or Google's App Engine. The benefit of this approach is that you don't have to worry about things such as servers, networks or storage. The downside to this approach is that you have no control over how these services are integrated into your existing infrastructure, and in some cases this isn't even an option.
In this scenario, you would write your application and then deploy it into their controlled environment, letting the PaaS provider manage the underlying infrastructure.
A Software as a Service (SaaS) is a service, that provides an application, rather than a framework. Examples of this would be Microsoft Office Live and Salesforce.com, that provide online mail and collaboration services. SaaS services typically are pre-written and do not provide the ability to change minor things such as themes or branding.