Finding similarity between two histogram plots
I'm curious what other people will say, but one option is to use KL-divergence.  If your two histograms have the same x-axis, you can divide every column by the total count to convert counts to proportions. Then you could treat the histograms as probability mass, and use the KL-divergence.  KL-divergence is really a measure of the distance between two probability distributions, but histograms are an approximation of a discrete distribution. You'd pick one of your distributions to be P and one to be Q, then calculate $-\sum_x P(X)\log{\frac{P(X)}{Q(X)}}$ where $x$ is each bin on the x-axis of the histogram.  Be aware that this distance metric is directional, meaning you'll get a different answer if you swap P and Q.  The reason is that the KL-divergence is a measure of information transfer (like, the information you gain by moving from Q to P), but I think that's irrelevant to your question.