40+ WAR Career: Player must have 40+ Baseball Reference WAR in their career. When paired with a team, must have played at least one game with that team in their career. Can be 40+ position player WAR, pitching WAR, or both combined.
6+ WAR Season: When paired with a team, 6+ Baseball Reference WAR must be achieved with that team in a single season. When paired with a non-team category, does not need to be in the same season. Can be 6+ position player WAR, pitching WAR, or both combined.
Note that, because of the "6+ position player WAR, pitching WAR, or both combined" qualifier, pitchers will not be marked as incorrect if they have at least 6.0 pitching WAR in a season, but less than 6.0 combined WAR because of negative WAR from hitting. For example, if a player had 6.1 pitching WAR and -0.2 WAR from hitting, leading to an overall WAR of 5.9, they will still be accepted for the 6+ WAR category because their pitching WAR met the 6+ WAR threshold. The same note applies for career statistics.
Also note that historical WAR values can change due to park factor updates and new play-by-play data for old seasons from Retrosheet. In some cases this may mean that a player moves from one side to the other of the 40 career WAR / 6 season WAR threshold. Check out the Sports Reference blog for updates to historical WAR values, which are typically rolled out in March each year: