What's the difference between the Gabor and Morlet wavelets?
The Gabor wavelet is basically the same thing.  It's apparently another name for the Modified Morlet wavelet. Quoting from Wavelets and Signal Processing:


  [The Modified Morlet wavelet] does not satisfy the admissibility
  condition but is nonetheless commonly used.  Sometimes this wavelet is
  called the "Gabor wavelet," but that term is improper because Gabor
  had nothing to do with wavelets.  He was ... one of the founders of
  time-frequency analysis.


That book is a collection of papers, and that paper ("The Wavelet Transform and Time-Frequency Analysis") is by Leon Cohen (of time-frequency distribution "Cohen class" fame), so I think it's reasonably authoritative.  

At the very least, it sounds like the confusion is just a naming disagreement.  According to A Friendly Guide to Wavelets (pg. 114), Gabor was the first person to propose the use of Gaussian windows for time-frequency localizations, so his name tends to get attached anytime they're involved.