People have also used “statistical physics” to refer to the former concept since forever. For example Landau.

“Statistical mechanics” is also used in a broad sense, just like “quantum mechanics” is often used for anything “quantum”.

What I'm getting from this discussion is that we use Statistical Physics to refer to anything covered by Statistical Physics AND Statistical Mechanics, while we use Statistical Mechanics in a narrower context, but it is also possible that some use SM loosely.