Many ThankU to Dear Sirs......... May I also ask then why different writers/professors/researchers are heavily using the word "Stochastic" rather than "Random", as per Signal Processing context........ In MATLAB or different DSP softwarse, there is no point of adding "Stochastic Noise", they all are using the word "Adding Random Noise" in their software coding.............
Summary from other answers for the same question, I think that random maybe means more like arbitrarily selected or given, while stochastic means more like that the procedure in a process gives unpredictable value(s).