gabor wavelet and gabor transform
The Gabor wavelet is (almost) the same as the Morlet wavelet (some authors distinguish these two by an additional constant to fulfill the wavelet's admissibility condition). And yes, it is the same function as in the Gabor transform (gaussian windowed oscillation).

The application of phase coherence should be independent of the underlying wavelet and the nature of the transform (Wavelet, Gabor/STFT, other weird metrics). Essentially important is the concept of reproducing kernels and the intrinsic (Heisenberg) uncertainty that influence you measure of phase coherence and must be taken care of.