The term for a penalty where a player is sent off for two minutes for a minor infraction is a minor penalty.
A minor penalty is hockey’s standard punishment for less severe rule violations, including tripping, hooking, holding, interference, slashing, and roughing. The penalized player must sit in the penalty box, and the team usually plays short-handed while the opponent has a power play.
A minor penalty normally lasts two minutes. If the team on the power play scores, the penalty usually ends early, although special situations such as coincidental penalties can change how the time is administered. A double-minor is different: it lasts four minutes and is treated as two consecutive minor penalties.
The other options describe more serious or different disciplinary categories. A major penalty generally lasts five minutes, a misconduct keeps a player out for ten minutes without automatically making the team short-handed, and a game misconduct ejects the player for the rest of the game. The two-minute minor penalty became standard in the NHL during the 1921–22 season.