please note there's precedence https://www.mathpages.com/home/kmath216/kmath216.htm

the difference is i approach it through the lens of evidence, allowing more insights and connections.

also, bonus connections: kl divergence is the ln of the lorentz factor (log(gamma)), the Bhattacharyya coeeficient is 1/gamma, and Jeffreys divergence is velocity times rapidity!