Final answer:
The insignia for a Sergeant Major includes three chevrons above three arcs, while a First Sergeant's insignia has an added diamond indicating different responsibilities and roles in the military hierarchy.
Step-by-step explanation:
The primary difference between the insignia of grade of a Sergeant Major and that of a First Sergeant in the U.S. Army pertains to the symbols used to represent each rank. A Sergeant Major typically has insignia featuring three chevrons above three arcs, while a First Sergeant's insignia has the same three chevrons above three arcs but with a diamond in the center. These symbols indicate their respective roles and responsibilities within the military hierarchy. The Sergeant Major often serves as an advisor to officers, whereas the First Sergeant is more directly responsible for the well-being and training of enlisted soldiers within a company.