In an interesting article Gregor Hohpe(Google Architect of EIP Fame) describes how EAI patterns and concepts can be used while building mashups.
This to some extent justifies, why major vendors in the EAI space (ex. TIBCO - GI Acquisition) are looking for offerings in this space.
It is not simple to differntiate Mashups from Composite Apps.Conceptually they are the same.Only difference is in their scope.Mashups are often built ad-hoc and then integrated using simple protocols like RSS and Atoms. Mashups are used in the context of Web 2.0. Mashups pull data from different sources, aggregate and transform the data to be used in different contexts.
Mashups: REST/XML,JSON, ad-hoc, bottom-up, easy to change, lowexpectations, built by user
Composite Apps: SOA/WS-*, planned, top-down, more static, (too) highexpectations, built by
If you want to know more about Mashups, have a look at this tutorial from the same author.
Heard of Yahoo Pipes.. . Experiment with it and have fun.