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What is the difference between the Monte Carlo (MC) and Monte Carlo Markov Chain (MCMC) method?

The goal of both methods seems to be to derive an estimate of a posterior/target distribution. If a process model exists which links some input parameters (which are themselves uncertain and can be described by a PDF) to an output parameter through a model equation or other computations, why would one choose one method over the other? Would both be applicable? Can one make a statement on the benefit of one method over the other with respect to the number of required draws/simulation runs in order to reach a sufficiently good approximation of the target PDF?