Unrelated Effects

This occurs when an object or action produces an effect that should be impossible for it to cause. This is often used to make something appear more powerful, or to display a character's skill. For example, a swordsman may slash his sword... and the victim explodes. Or a gunman shoots... and his target is sliced cleanly in half. The effects themselves are never explained, by real physics, story physics or special abilities (such as Chi/Psi/Magic). If the swordsman's victim was wearing a backpack full of dynamite, or if the gunman's target is cut in two with a ragged line of bullet holes, those situations would not be examples of Unrelated Effects.

One of the most common types of Unrelated Effects is a shining light. An especially strong attack will release a bright glow, completely unrelated to incandescence, reflecting sunlight or any light-producing object. A fist will glow for the punch, a light will shine just before an explosion, or a light trail will follow a sword.

Quite often, this can be the result of Special Effects taken too far. Loosely related to Made of Explodium, where the effect is unrelated but often expected anyway.

Anime and Manga

 * This is common in Shounen series. Cooking manga seems to be the biggest offenders, but practically any series where the main characters are engaged in a duel of skill will have an example of this trope.
 * In Hikaru no Go, when someone is demonstrating exceptional skill in the game, their fingertips glow as they place down the stone. Somewhat over-dramatic for a manga/anime about a board game.
 * Another board game example is Saki. For starter, the titular character spouts lightning from her left eye when she puts down a Mahjong tile. One of her most terrifying opponent can create the illusion of drowning in the ocean as she draws a tile. Another turns into cackling Psycho Lesbian angel (sic).
 * Pokémon overuses the "shining light" variety. Any attack involving a body part causes that part to glow, beam attacks charge by Sucking-In Lines, and anything that's about to explode shoots out rays of light.

Tabletop Game

 * Dungeons and Dragons
 * Forgotten Realms has a justified In-Universe case. The Menzoberranzan AD&D2 boxed set introduced "frills" -- bogus rituals, spell components and special effect cantrips made to look as parts of the spell. Drow wizards use this to mask from unwanted observers identities, properties and sometimes nature of their spells. As an added bonus, this misdirects enemy plans based on spying, as under duress the wizard can drop all unrelated act and cast the same spells much faster. And with perverted sense of humor it's worth kissing a frog if your rival will have to repeat it every freaking time while trying to figure out what he does wrong.
 * 3e Magic of Faerun introduced Spell Thematics feat, which adds some cosmetic feature (like wailing skulls or lightning sparks) to appearance of spells, which makes them harder to identify, and slightly boosts power of tweaked spells.
 * 3.5 Sourcebook Complete Scoundrel introduced something similar for more generic use as "False Theurgy" magical Trick -- using Bluff or Sleight of Hand skill to disguise a cast spell as another (until visible effects, if any, give it away).

Western Animation

 * Aqua Teen Hunger Force: Pretty much anything which Master Shake throws to the ground explodes quietly; it's rarely reacted to, never really commented on, and entirely unexplained.