Wavelet Transform and STFT
In the STFT, you apply windowing and Fourier transform on the signal using sliding patches and then combine the resulting transforms, which will help you eventually end up with a uniform time/frequency representation of the signal.

In the wavelet transform case, you apply a filter bank on the overall signal at once. In this way, you obtain a coarse-to fine resolution pattern on the time/frequency representation.

Both methods result in similar time/frequency representations which can be derived from each other.

The major differences: 
(1) STFT is uniform yet CWT is not. 
(2) You apply STFT on patches, but you apply CWT on the overall signal.
(3) STFT involves Fourier transforms but CWT only requires an orthogonal filter bank.