From the game's encyclopedia
A character's family consists of their Close Family Members and Extended Family Members.
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.
Family is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A character's family consists of their Close Family Members and Extended Family Members." It covers Close Family and Extended Family. The game also links it as Family Members and Family Member. 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.