Upon use, the user drops a sphere of electricity diagonally downwards, which can deal medium damage as it falls. If it lands on a surface, it turns into an arcing wave of electricity that hops along the terrain's surface and deals slightly less damage. The projectile will wrap around corners and snake along walls and even ceilings if the corners are not too sharp and it lives long enough; it cannot wrap around the underside of soft platforms due to there being no ceiling to latch onto. When the move is used on the ground, it essentially turns into the wave form immediately.
Special Move customization was introduced in Super Smash Bros. 4. Thunder Jolt's variants are:
Unlike most other attacks Pokémon use in the Super Smash Bros. games, there has never been an attack named Thunder Jolt in any of the Pokémon RPGs. Thunder Jolt was, however, present on the original Pikachu card as one of the many moves invented for the Pokémon Trading Card Game (TCG); both the English and the Japanese names on the card match the Smash move's name in the respective versions of Smash Bros.. The name of the move in the Smash Bros. games likely arose from the popularity of the trading cards at the time of Smash 64.
The move itself does show up in the Pokémon: Indigo League season episode The Problem with Paras, where Pikachu is ordered by Ash to do a very weak ThunderShock. This results in a very tiny static shot that is almost identical to the move shown in Smash.
Its custom versions, however, are actual moves in the Pokémon games and match their effects accurately. Thunder Wave does no damage, but always inflicts the Paralysis status unless the target is a Ground-type Pokémon, is naturally immune to Paralysis, already has a major status aliment or is protected by Substitute or Safeguard. Thunder Shock is a basic low-level Electric-type attack, with 40 base power and 100% accuracy. Both moves can be learned by Pikachu in all main series Pokémon games.
Use this ground-hugging projectile attack while standing or jumping.
Description from the Brawl Instruction Booklet
Release a jolt of electricity that moves forwards by bouncing along the ground. Also usable in midair.
Description from the Super Smash Bros. for Nintendo 3DS Foldout
Fire bouncing balls of electricity.