Regimental Sergeant Major

I'm looking into my family tree
My grandfather, in his personal Military records, was reffered to as a Sergent Instructor.
Excuse my ignorance but is this the same as a sergent Major?
The reason I ask this is:
When growing up until I left home there was a chest. It apparently belonged to my grandfather. On the side of it were the words "Sergent Major Ladbrook". I an my family are curious how this title came about.
Signed Warren Ladbrook