I have only heard of two types of teams:
Blue team - The defenders of a network
Red team - Attackers of a network
Tiger team - Same as red team, however is a older term of the attacking/opposition side of an engagement
White team - The team that establishes the rules of engagement and are usually the employees of the organization. The white team does not conduct any testing.
CISSP study guide has the following explanation of the different teams:
White team A neutral team of employees acting as observers, referees, and judges between > a red team of mock attackers (offenders) and a blue team of actual defenders of their
enterprise’s use of information systems. The white team establishes rules of engagement
(ROE) and performance metrics for security tests. The white team is also responsible for
deriving lessons-learned, conducting the post engagement assessment, and communicating
results to management. Occasionally, the white team also performs incident response
activities and addresses bot attacks on an emergency basis.