The rank structre says they are on the same level, but whats then the differnt between these two? Or is ist just another term for the First Sergeant?
Orderly sergeant / covering sergeant is a "job" in the drill books. He covers the captain. that is, stand behind him and take over his position in the formation when he moves to the front or rear of the company.
1st sergeant is a rank.
In the infantry he is responsible for all the paperwork and that the day to day life in the company work as it should.
In the cavalry and artillery they also have a quartermaster sergeant and a Commissary Sgt. So they had 3 men to do the same work.
(with all the extra company gear, like guns, and all the horses it makes sort of sense)
Similar the rest of the sergeants got the same rank.
but the 2nd sergeant in combat/drill is the left guide of the company and got a different job than the rest of the sergeants.
But the rest of the time they all have the same jobs.
So one is a job during drill and in combat.
The other is a rank and administrative position that that have a long list of tasks to make sure gets done every day.
Part of this difference might very well be the fact that the drill books are word for word translations of the French 1845 drill.
The number of corporals and sergeants and even number of companies in the battalion might also not fit, depending on if we are talking Hardee, Casey's or other drill books. (and if we are talking a US volunteer regiment or a regular one)