What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?
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.