Randomness coming from the environment (for example, brownian motion, but also hardware random number generators)
Randomness coming from the initial conditions. This aspect is studied by chaos theory, and is observed in systems whose behaviour is very sensitive to small variations in initial conditions (such as pachinko machines, dice ...).
Randomness intrinsically generated by the system. This is also called pseudorandomness, and is the kind used in pseudo-random number generators. There are many algorithms (based on arithmetics or cellular automaton) to generate pseudorandom numbers. The behaviour of the system can be determined by knowing the seed state and the algorithm used. This method is quicker than getting "true" randomness from the environment.