It is similar to [Avenging Wrath] by the fact that both spells increase the paladin's damage for a few seconds. However, there are important differences between them which heavily differs their usage.
Inquisition only increases damage. Avenging Wrath increases both damage and healing.
Inquisition has, in contrast to Avenging Wrath, no cooldown. This is possibly the largest difference between them, allowing Inquisition to be active at all times. This makes it similar to a rogue's [Slice and Dice] or a druid's [Savage Roar], being intended to generate a constant buff which increases the paladin's damage. To Retribution-paladins, Avenging Wrath may be considered a long-cooldown extension of this, similar to the mage's [Arcane Power].
Trivia[]
The level 81 spell for paladins in World of Warcraft: Cataclysm was originally planned to be Blinding Shield, but it was replaced with Inquisition before patch 4.0.1 went live.
Patch 8.0.1 (2018-07-17): Re-added as talent. Increases damage and Haste by 8%, and last for 15 seconds per Holy Power (was 30% Holy damage and 10% critical strike, lasting for 20 seconds per Holy Power).
[Inquisition]. For lore about inquisitions, see Inquisitor (occupation).
[Avenging Wrath] by the fact that both spells increase the paladin's damage for a few seconds. However, there are important differences between them which heavily differs their usage.
[Slice and Dice] or a druid's 
[Savage Roar], being intended to generate a constant buff which increases the paladin's damage. To Retribution-paladins, Avenging Wrath may be considered a long-cooldown extension of this, similar to the mage's 
