There is Compression done by Prediction by partial matching [0]
There is the Kolmogorov Complexity [1], Normalized Information Distance [2] and Normalized compression distance [3] that correlates those.
Finally, there's the Pre-Big Bang Informational Compression and the Delayed Release of Antimatter [4]
All big {rabbit/black} holes to lose some time, if you have any.
[0] https://en.wikipedia.org/wiki/Prediction_by_partial_matching
[1] https://en.wikipedia.org/wiki/Kolmogorov_complexity
[2] https://homepages.cwi.nl/~paulv/papers/chapter08.pdf
[3] https://en.wikipedia.org/wiki/Normalized_compression_distanc...
This is exactly why I think they are one and the same. It's relatively trivial to just plop a (lossy) machine learned markov chain instead of one learned (perfectly) from the data into PPM. With zero changes to the rest of the algorithm.
I'll add Minimum Description Length to the mix. Under certain definitions and conditions, it equals the Bayesian Information Criterion plus an extra term, which I consider a very interesting result in this "two faces of the same coin" perspective.