I'm a bit slow today but I'm not sure I got what the GIF was about. It is well known that the mean (1st moment) and stdev/variance (2nd moment) are insufficient to uniquely describe an arbitrary probability distribution except in the case of the normal distribution.

Therefore it shouldn't be surprising that that you can find probability distributions that share the first two moments, but differ wildly in the higher moments (skewness, kurtosis) or even the number of modes (bimodal, trimodal, etc.).

Not everything in the world is Gaussian, but we knew that.