I guess this never registered with me when I read the Feynman Lectures on Physics in the past. But I have wondered, from time to time, what distinguishes statistical mechanics from, say, kinetic theory.
Like most people, I assumed the distinction was that statistical mechanics is a probabilistic treatment of thermal physics. Thermodynamics deals with heat at a macroscopic level using concepts such as "heat flow" and refinements of the ideal gas law, etc. So that's different from kinetic theory which deals with concepts of actual molecular motion. To my mind, I always thought of statistical mechanics filling in the the middle part between kinetic theory and thermodynamics.
But, notice what Feynman says statistical mechanics is:
We have discussed some of the properties of large numbers of intercolliding atoms. The subject is called kinetic theory, a description of matter from the point of view of collisions between the atoms. Fundamentally, we assert that the gross properties of matter should be explainable in terms of the motion of its parts.
We limit ourselves for the present to conditions of thermal equilibrium, that is, to a subclass of all the phenomena of nature. The laws of mechanics which apply just to thermal equilibrium are called statistical mechanics, and in this section we want to become acquainted with some of the central theorems of this subject.
Considering Feynman held the Richard C. Tolman professorship in theoretical physics at the California Institute of Technology, I tend to take his characterization of statistical mechanics seriously. That is, considering Tolman wrote "the book" on statistical mechanics: The Principles of Statistical Mechanics, By: Richard C. Tolman
So what is the proper definition of "statistical mechanics"?