note that these are not exclusive. you could divide ML into a traditional statistical approach and a probabilistic one that is concerned with deriving the underlying probability distribution. probabilistic programming is kind of like a domain specific language for achieving this. there is also differential programming that works on the same principle. there are certainly industrial usages of this paradigm. look up pyro (http://pyro.ai/examples/intro_part_i.html) for ppl and jax (https://github.com/google/jax) for differential programming