I do think there's some value in being able to tersely express your exact point to a peer.

For example "a random process" could mean "any process in existence" whereas "a stochastic process" clearly states stochastic as being a property of the process.

I however agree that things can sometimes get a bit wrapped up in sounding cool just to sound cool.

As a rule of thumb you should never use a big word when a diminutive word will suffice.

Among the meanings of random are:

1. Stochastic.

2. Unbiased.

3. Typical and average.

4. Unprompted or unjustifiable.

5. Habitually using non sequiturs.

So, I might use a random sort algorithm like, I don't know, heapsort. Or I might be reading through some code and find a random sort algorithm --- why is there a mergesort in the middle of this calendar routine? Or, if you want a random sort algorithm, you should be sure to use the Fisher–Yates shuffle. Or, to avoid the quadratic worst case of treesort and quicksort with high probability, you can convert them into random sort algorithms by picking partition elements randomly.

Of these four random sort algorithms, only the fourth is stochastic. (I haven't figured out how a sort algorithm could habitually use non sequiturs.)

I think that one doesn't come from being fancy, but from machine learning being the terminologically-uncomfortable collision between statics mathematicians and computer scientists, who previously had essentially no cross-talk with each other. There's a number of similar places where ML uses statistics terms rather than ones you'd expect from a computer science (as a branch of mathematics) heritage.

This makes sense to me. Thanks for the insight!

You're still using stochastic processes? I switched to aleatory ones after reading a DeepMind pre-print that's been going round.

These aren't synonyms.

Random is a property of the world itself; stochastic means "we allow ourselves to think of this process as random because we can't/don't want to deal with it exactly".

Following this is the difference between Random Differential Equations and Stochastic Differential Equations.

I like Robert Anton Wilson's definition. "A stochastic process is a random series, but it is a special kind of random series. In a stochastic process, some agent or agency is making selections—picking out of the randomness a pattern that is not random."

Are the terms that interchangeable? "I used a random algorithm" is a different expression from "I used a stochastic algorithm". For me, the term stochastic is one half of the stochastic vs deterministic categorisation.

I think that's orthogonal to the original question