wave file size discrepancy?

I exported a song from Sonar using 320 kbps MP3, and "keep wav file" to put onto a CD for demo purposes.
Then I brought the Wav into Audacity to bump it up with Normalize. 
(I can usually get a few more DB that way).
Then I exported the result, again to Wav (Microsoft signed 16 bit)
The stereo Audacity Wav file is one half the size of the Sonar Wav file.

Is this a compression result or just that Sonar uses 32 bit?
Wouldn't the smaller 16 bit file have noticeable less quality?
If so, would there be a better format to export with from Audacity for CD quality?
They seem to have them all. (13 choices) but they don't specify the bit rate.
Or is there a better way to bump the file (normalize). In Sonar?

Thanks once again Dave.
Glenn