The core of Monte Carlos methods is repeated random sampling

Monte Cardo methods can be used to verify statistical/probablity theories.

Any numerical procedure involving random sampling can be called Monte Carlo method

Monte Cardo methods can be used to estimate the sensitivites of a calculation to random errors.

When realizing Monte Carlo in coding, the random sampling/sample generation code should be outside the for loop

Monte Carlo method is a numerical method

Monte Cardo methods can be used to estimate random output of a system with random inputs.

Monte Carlo is an analytical method.