Approximate Bayesian Computation VS Monte Carlo Simulation
Yes, ABC is a specific application of Monte Carlo method. That application is approximating likelihood functions.

Anything that happens in a computer is actually deterministic. However, ABC, like any other MCM, must have a good pseudo-random generator. There is no difference in the amount of randomness required by the methods.

Examples of Monte Carlo methods which are not ABCs include genetic algorithms and Monte Carlo integration.