Wikipedia states that stochastic means random. But there are
differences depending on the context.
Stochastic is used as an adjective, as in stochastic process,
stochastic model, or stochastic simulation, with the meaning that
phenomena as analyzed has an element of uncertainty or chance
(random element). If a system is not stochastic, it is
deterministic.
I may consider a phenomena is a random process and analyze it
using a stochastic simulation model.
When we generate numbers using a probability distribution, these
are called random numbers, or pseudo random numbers. They can also
be called random deviates.
See related links.