First sergeant
From Halopedia, the Halo wiki
First Sergeant is the eighth enlisted rank of the UNSC Marine Corps and the UNSC Army, and equal in pay grade to Master Sergeant, although the two have different responsibilities. First Sergeant is equal to the rank of Senior Chief Petty Officer in the UNSC Navy. It is a staff non-commissioned officer (SNCO) in the Marine Corps and a non-commissioned officer (NCO) in the Army.
First Sergeant and Master Sergeant
For the United States Marine Corps, in their annual performance evaluations, eligible Gunnery Sergeants indicate whether they wish to be considered for promotion to Master Sergeant or First Sergeant, and thus whether they enter the promotional track for Master Gunnery Sergeant or Sergeant Major. Once promoted, the promotional track is permanent; lateral movement between the two programs is not possible.
One of the major differences between the two ranks is that First Sergeants have a general command status, while a Master Sergeant's role is as a provider of technical military leadership.
Whether this carries over into the UNSC Marine Corps is unconfirmed.
Responsibilities
Assuming the rank still exists, First Sergeants function as the senior NCOs for company level units. They advise and assist the company commander directly. Although technically the same rank, they are given more authority than Master Sergeants.