The most visible difference between adventure games and walking sims is the removal of puzzles, although this evolution has happened across many genres of game, as radically extending play time through mental frustration fell out of fashion (to be replaced, of course, by grinding, cooldown timers, and other more modern mechanisms of inflating playtimes).
Adventure games and walking simulations vary in the gameplay. I like that walking simulations are more lowkey and don't always have a "purpose or goal" for the game, but they allow the player to truly immerse themselves into the simulation. Adventure games are often more violent, which is not something that every player enjoys.