The fourth Gym Badge you’ll earn in the game depends on whether you’re playing Pokémon Sword or Pokémon Shield. If you’re playing Pokémon Sword, you’ll be fighting for the Fighting Badge; if you’re playing Pokémon Shield, you’re instead going for the Ghost Badge.
You’ll fight a different Gym Leader and a different Gym Mission depending on the game you’re playing, too, but mostly everything else up to the Stadium will be the same, so don’t worry too much about the differences throughout the entire section — it will cover both games unless it specifically says otherwise.