So is Airtunes vs. Airplay ...is it just re-branding?

It is kind of. Airtunes required airport express and it was only audio. Now it is compatible with audio/video and can go directly from computer to ATV or iphone/ipad/itouch to ATV .

You can stream from your iphone to apple tv, but currently there are limitations. It will expand as time goes on.

The additional features of Airplay like streaming video and being able to stream from your iPhone directly to the Apple TV came with the new 2nd generation Apple TV. Your 1st generation Apple TV does not support the newer Airplay features. It only supports the "Airtunes" features it always had.

AirTunes and AirPlay are not the same. AirTunes allows you to stream audio from iTunes or an ATV to an AirTunes compatible audio device, whereas AirPlay allows you to stream audio and video from an iOS 4.2 device (like an iPhone or iPad) to an ATV2, and audio from an iOS 4.2 device to an ATV1 (once they fix the iOS AirPlay bug that fails to recognize an ATV1).