Game concept
Directed Great Holy War
The game also links it as Directed Great Holy Wars, Jihad, Jihads, Directed.
From the game's encyclopedia
A Directed Great Holy War is declared by a Temporal Head of Faith with the intention of bringing a Kingdom under their own rule.
Rulers of their Faith might choose to assist the Head of Faith, and may get rewards from doing so. Rewards include Piety and potentially having their Dynasty become Landed within the conquered Kingdom.
Rulers of the targeted Religion may choose to defend against this war without the need for an Alliance.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Directed Great Holy War is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Directed Great Holy War is declared by a Temporal Head of Faith with the intention of bringing a Kingdom under their own rule." It is part of Great Holy War. The game also links it as Directed Great Holy Wars, Jihad, Jihads and Directed. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.