I believe that you're on the right track with your thinking.
At our company, we use the phrase "Composite Application" to encompass this idea of combining existing applications / services / data into a new application / data view. As you've pointed out, Mashups are one type of composite application--it happens to be a dashboard application. Contrast this with a dashboard built into an ERP system that reports only on the data within that one system--this would also be a dashboard application but would not be a composite application.
In addition to mashups, we also identify another type of composite application: the "Composite Process." A Composite Process combines existing applications / services / data into an application that executes a business process, whereas dashboards (mashups or otherwise) report rather than execute. For example, "Order-to-Cash" is a common business process, and we built an "Order-to-Cash" application out of 4 existing applications / services. Our new application is thus a Composite Process. We also hope to build a Mashup that will be our dashboard reporting on the same process.
As you have mentioned, Service-Oriented Architecture (SOA) is one way of architecting a Mashup or any other composite solution. SOA makes it easy to combine the existing applications because they are already exposing their functionality or data via their Services. You could (not that you'd want to) also architect your combined solution in a non-Service-Oriented way--it would still be a composite application even without the SOA.
Hope that helps!
Enterprise Integration, Inc. (EII)
In continuation to Scott's comments, I would like to add a bit more on the mashups or MashApps. These , infact can go beyond the Dashboards and can become complete applications by themselves. Infact, one of the new fads is to consume mulitple services and create totally new apps out of them (aka composite apps).
Companies like CordysProcessFactory and RunMyProcess are very much into mashapps and solid proponents of Paas (which in a way forms the basis for Mashups).
As SOA applies to technology and frameworks, Mashups are for end apps. A classic example could be iGoogle.
Most of the BPM companies are letting the complex processes to be converted to webservices. So consuming the webservices and creating a totally new application makes the mashups very powerful if perceived from that perpective rather than from pure Dashboard perspective (or as KPI modeller).
Hope this helps