>>I think the French mathematicians (Bourbaki, maybe?) introduced a distinction between aleatory and stochastic. Aleatory (as in "alea iacta est") is something that gives a random event from a predefined discrete set of possible events, as in a cast of dice or toss of a coin. Stochastic would take any possible value from an infinite set of real (or complex) values. The set may be limited, but not finite.
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>Before reading your message, I hadn't even known the meaning of the word "stochastic" (although I did hear about Nicholas Bourbaki).
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>The Wikipedia article on "stochastic process" seems to use it more or less as synonymous to "random".

It's more or less the same. If something is stochastic, it means it's based on chance.