Civilians assign too much importance to rank; military people know that it’s the position that counts. They don’t look at a bunch of NCOs and think, here’s a Sergeant Major and here’s a Sergeant First Class and here’s a Staff Sergeant, they think: here’s the senior radio technician, here’s the quartermaster, and here’s the 2nd platoon sergeant. A rank may be a *prerequisite *for a position, but it isn’t a position.
That was also my understanding.
First Segeants and Sergeants Major get the full-court title out of respect; Master Sergeants (also E-8 just like a First Sergeant) are not addressed as “Master Sergeant,” just Sergeant.
The First Sergeant is the cornerstone of the U.S. Army. The Sergeant Major is a First Sergeant with experience (and since First Sergeants tend to be scary experienced, that’s saying something).
The Sergeant Major typically serves as the senior enlisted at battalion-level and above.
To continue your “construction crew” metaphor, the First Segeant might be a site supervisor/foreman, in charge of multiple crews at one location, and a Sergeant Major a project foreman, in charge of multiple sites.
As U.S. Army sergeants go, there’s only one of these at a time: Sergeant Major of the Army - Wikipedia