They are different things: stochastic processes are probabilistic, so yes, random, but not without limits rather applied in specific frameworks.. relevance: In a simulation, were one to model artificial intelligence, one could apply stochastic processes (eg stochastic neural networks).
Indeterminacy can also mean incompleteness or 'unknown' (aka an indeterminate model is one where some thing remain unknown, therefore the model is.. duh, indeterminate). I am therefore making it clear that a simulation need not be deterministic, but by indeterminate and random I mean organized stochastic processes.
The other reason I brought up indeterminacy was the classic 'free will problem' that says that if the universe is determinate, there is no such thing as free will, because you can predict everything in advance. If a simulation is determinate, there can be no free will in the simulation. So I bring up 'indeterminacy' not just in the above context, but also to indicate that the simulation can be all those things, and we still have a free will problem. Lastly the 'being' in the simulation does not know whether or not he is in a simulation. In a roundabout way the poster a step up from the one I am responding to almost brings up Descartes' dream argument... sans the cogito ergo sum, of course the simulation throws the whole cogito ergo sum in doubt anyway, perhaps... but I digress.
Anyway I don't assume that the other poster knows what the word stochastic means either (you yourself think it just means 'random'), so between using those three descriptors, maybe something will be communicated, assuming the other poster isn't looking for quick and easy ways to be snide aka 'did you think it would be more convincing?'