Zap is the uncharged version of Hero's Side Special. It's a small shock that costs very little MP and travels a short distance from Hero's sword instantly upon pressing the button. It deals little damage and practically no knockback, but can be a reliable source to hit an opponent quickly and then try to use a Dash Attack or Forward Smash to deal more damage.
Zapple is the medium-charged version of Hero's Side Special. It causes a bolt of lightning to travel a considerable range from Hero's sword instantly when the button is released and hit opponents for some pretty good damage yet practically no knockback. As the attack is fast, it can be easily used to deal some damage to your opponents when they're further than your usual attacks could reach, but isn't suited for finishing someone off.
Kazap is the fully-charged version of Hero's Side Special. When the charge requirement is met (which is surprisingly short for a charge attack like this) a bolt of lightning will fall from the sky towards Hero's sword, ignoring any ceiling above Hero. Once the bolt reaches Hero, he will spin around with his sword after a short delay, hitting any enemies in front and behind him. An enemy hit from close range from the start of the attack until the end will take 38% damage and suffer considerable knockback, making it a reliable kill move. However, it has considerably less range in one direction than Zapple does (which is supposedly compensated by being able to hit enemies behind Hero) and costs a very large amount of MP. It's risky as it's easy to miss, but very rewarding if it hits its target. The bolt of lightning that falls from the sky can also be used to deal damage to opponents directly above Hero, similar to Pichu and Picachu's Down Specials. However, the lightning bolt only deals 10% damage and isn't worth the extremely large MP cost.