Do you think part of the problem might be the definition of stochastic? Basically, it just means 'random', but then there are stochastic processes that have more mathematical structure and theory behind it.
Similarly, the use of concepts like Monte Carlo. Some people just use it to mean random, but there is also a well-defined mathematical theory behind it as well.
I probably don't need to be telling you any of this...
Applied mathematics is harder than pure. (Been there, done both.) Not to mention numerical analysis and coding implementations. Euclid's book on circles doesn't help where the rubber meets the road.