Quick Guard- is an alternative to Protect. Unlike Protect, which works on all moves, Quick Guard prevents all effects from moves with a heightened Speed Priority. In addition to that, it also protects all the player's Pokémon on the field rather than just the user.
Wide Guard- is another alternative to Protect. However, Wide Guard protects against specific moves, specifically moves which have more than one target such as Surf & Earthquake. In addition to protecting the user, it protects all of the user's allies in battle for that turn.
So Quick Guard protects against move with priority like Quick Attack,Aqua Jet,Mach Punch. Wide Guard protects against moves that hit more than one target like Earthquake,Surf,Lava Plume