See here for why and in which way nondeterminism and randomness are not the same!

Fitting category tags are automata and/or computation-models. Other related tags include finite-automata, pushdown-automata, linear-bounded-automata, turing-machines, cellular-automata, formal-grammars, and probably more.

Note that in the context of grammars, nondeterminism should not be confused with ambiguity, either!