I don't think there's universal agreement about terminology, but to many of us who work in the area, Monte Carlo (MC) means specifically using random sampling t

I don't think there's universal agreement about terminology, but to many of us who work in the area, Monte Carlo (MC) means specifically using random sampling to estimate a deterministic quantity. For example, MC methods can be used to compute the ground state energy of atoms and molecules. This in principle can also be done by solving the many-body Schroedinger equation, but direct numerical solution is simply not feasiable except for systems with very few degrees of freedom. In contrast, the term "simulation" often (but not always) means to simulate to take a look. As is usual with these things, the boundary is not sharp. One selling point of sampling is that with greater expense you also get more information about the "energy landscape," can do uncertainty quantification, etc.