There is a distinction. Usually statistical mechanics means the ensemble theory and partition functions that connects microscopic systems to macroscopic ones from material point of views. However, statistical physics is a bit more generic, for example complex networks may not use ensemble theory or partition functions and could use only statistics on the network, such as average neighbourhood or similar.

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”.