Final answer:
The two types of non-judicial punishment proceedings are Summary Court-Martial and Article 15, which provide a way to discipline military personnel for minor offenses.
Step-by-step explanation:
The two types of proceedings taken during the non-judicial punishment process are Summary Court-Martial and Article 15. A Summary Court-Martial is a simplified military court proceeding meant to resolve charges of minor offenses committed by enlisted members of the military, which does not rise to the level of the General or Special Court-Martial. Unlike a Summary Court-Martial, an Article 15 proceeding allows for a commanding officer to discipline enlisted personnel without the need for a formal court proceeding, offering a more streamlined and less formal corrective process for minor infractions.