Random or Stochastic
Definitions
The following definitions are abbreviated from Lexico.com q.v. for more detail.
Random
In a formal statistical sense, governed by or involving equal chances for each item. Less formally, made, done, or happening without method or conscious decision
Stochastic
Having a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely.
Evolution is Stochastic
Randomness relates to possible outcomes of variables, such as throwing dice. A stochastic process is a whole collection of random variables in a "probability space" i.e. the set of all possible outcomes — the word "space" is metaphorical. Evolutionary change depends on random events at the level of reproduction and mutation, against the much larger background of the environment in which reproduction takes place. Thus it is incorrect to consider evolution as merely random: in fact living things thrive or struggle according to the environment that they find themselves in, and minute random reproductive events can make a difference to the survival of individuals and their offspring.
Failure to appreciate the stochastic nature of the evolution of species gives rise to the error of thinking that random mutations cannot generate all the genetic information required for irreducibly complex structures, for example as argued here.
A very informative lecture Randomness and Other Metaphors in the Theory of Evolution given at a conference "Evolution and Christian Faith" by Ard Louis (a mathematician and professor of theoretical physics at Oxford) is on Youtube.
