Why are the Continuous Wavelet Transforms of the same signal drastically different?
There are differences in axis-scales. However, I suspect that the main difference is that the first picture relates to either a real CWT (or time-frequency transform) or the real-part of a complex CWT (or time-frequency transform, again), while the second seems to be a magnitude.
In the first  image, the apparently wiggling part could &quot;planified&quot; by combining it to some imaginary part. Then changing the $y$-scale from linear to logarithmic could make the plots look closer.
Apart from representation issues (scales, magnitudes), with admissible continuous wavelets, there exists a wide variety thereof.  Factors that affect scalograms in practice are also the global shape of wavelets (symmetry and anti-symmetry for instance), their regularity, and the ways it is discretized (number and sampling of voices).