Application Server equals Middleware?

When I first encounter the Java 2 Enterprise Edition world, I encountered only application servers. Then some comparison news, publications, etc. would put all the application servers manufacturers as major middleware vendors. Then I had this equation on my mind:
application server == middleware

Then through further readings, experiences, discussions, etc I concluded that:
application server != middleware

They are of different kind level of abstraction! 

Some (Java) middleware parts are running on Java application server. But to make Java Middleware *EQUALS TO* Java Application Server, is a big big mistake that I have made.

The equation just doesn't seem to balance out...

These are components of middlewares:

Messaging

Integration Platform

Portal