Ajax - asynchronous?

I have always been curious about the asynchronous behaviour of Ajax. Is it really asynchronous? If it is, is it really being used that way?

This post by Peter-Paul Koch clearly expresses my curiosity.

Basically, the idea of asynchronous model is that the user is freed from the client-server request-response cycle and can perform other tasks 'while' waiting for a server response. I could appreciate the idea earlier but then later realised how often will I have (or want) to do 'other things' while I am waiting for the server to respond.

Some of the comments to this post point me to some good examples like :

1. Google Maps - Maps for nearby regions are being downloaded when I am looking at it. (pointed by Dan Knapp)
2. Chat Applications - You can recieve other messages and type at the same time. (pointed by Day Barr)

Some other examples that I could think of:

1. Gmail Attachments - they start getting uploaded even before I send the email.
2. Google Groups - I tried out the beta version that was released recently. I can play with the option, tools on the top while the a new page is being fetched at the bottom.

But still one thing that keeps on tickling me. Why is the asynchronous part made so prominent in the name? Doesnt the real power of ajax lies in the making HTTP requests from within the page and being able to update small parts without reloading the entire page?

Comments?