Where procedural games differ from walking simulators is in their lack of curation: they let you walk wherever you want, including perhaps into uninteresting places, rather than down a well-prepared path that tells a particular story
There is a clear distinction between procedural vs walking simulators. The main difference lies in the level of restriction. As procedural games let you go wherever, walking simulators have a path laid out. Essentially, procedural games provide a universe for exploration while walking sims prioritize feelings of emotion.