To elaborate a little more on Arjen's answer: mendix apps are not the same as java apps. They're mendix apps. Although the runtime happens to run on java virtual machine, mendix apps run on the mendix runtime (in this context, virtual machine and runtime are two virtually interchangeable terms).
So, to run a mendix app you need a mendix application server. There just happens to be only one of those application servers, which the techies refer to as the "m2ee server". This handles all of the application server level responsibilities, as well as managing the runtime which actually runs the model.
To actually answer your question: the business modeler produces .mda files, which are packaged mendix applications. These are the artifacts that you're after. Java application servers run .jar/.ear/.war files, mendix application servers run .mda files. These aren't interchangeable in any way, due to the fact that mendix runs "on top of" java, just as java runs "on top of" assembly language or whatever your JVM happens to be built on :)
The Mendix Business Server acts as an application server, so no need to deploy it into another one. It consists of several jars.