What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform? At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same.  Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, etc.  But maybe there's a difference that  I'm missing?

Constant-Q Transform Toolbox for Music Processing says:


  CQT refers to a time-frequency representation where the frequency bins are geometrically spaced and the Q-factors (ratios of the center frequencies to bandwidths) of all bins are equal.


Time-scale analysis says:


  That is, computing the CWT of a signal using the Morlet wavelet is the same as passing the signal through a series of bandpass filters centered at $f = \frac{5/2\pi}{a}$ with constant Q of $5/2\pi$.
Simply speaking both the const-Q-transform and the Gabor-Morlet wavelet-transform are just continuous wavelet transforms. Or, more precisely, approximations thereof, as there will always be discretization issues in real applications.

A property of wavelet transforms is that they have build in the constant Q-factor property, or in other words logarithmic scaling.
Gabor and Morlet are just two names of a particular wavelet function (complex exponentials with a gaussian window) which is used most commonly.
The CQ-transform just uses another basis function/wavelet and has a special name attached to it, probably to some historical reason.