From Halopedia, the Halo wiki
For the similar, but distinct player customization options seen in Halo 4, Halo: The Master Chief Collection, and Halo 5: Guardians, see skins.
Armor permutations are features in Halo 3, Halo 3: ODST, Halo: Reach, Halo 4, Halo 2: Anniversary, Halo 5: Guardians, and Halo Infinite that allow players to customize their multiplayer character's armor to their liking. Almost every game featuring this aspect of customization allowed players to change various pieces of armor worn by their multiplayer character. In Halo 3: ODST specifically, the player was allowed to choose members of Alpha-Nine to play as for the game's Firefight component. The player was still given color choices, and the option to play with or without a helmet was available.
In Halo 3, options were limited to helmets, shoulders, and chest plates, Reach added onto this selection and offered various helmet attachments, along with newly implemented wrist, utility, knee pad, and visor color options. Halo 4 would continue this trend, but instead of wrist attachments and leg utilities, offered full customization of both wrists and legs. Halo 5: Guardians regressed and only allowed players to swap full body armor sets and helmets.
Beginning with Halo 3, the player was allowed to swap genders for their Spartan in the form of a voice option. Halo: Reach, Halo 4, and Halo 5: Guardians would carry this forward with male and female player models being distinct, while Halo 2: Anniversary would drop the option.
In a unique twist, Halo 2, Halo 3, Reach, and Halo 2: Anniversary allowed the player to choose between being a Spartan or Elite. Halo 2 didn't allow for specific armor swapping, but Halo 3, Reach, and Halo 2: Anniversary featured varying levels of armor customization for the Elites. Halo 4 and Halo 5: Guardians dropped this aspect of player customization altogether.
Halo Online's customization requires players to purchase armor pieces with in-game currency similar to Halo: Reach.
For a more detailed article, see:
For a list of all cut permutations see: