We are probably all talking at cross-purposes, due to attempts to simplify loose and inconsistent terminology used some 200 years ago.
I had not realised that Fusiliers, like Rifles, used the title 2nd Lieutenants rather than ensigns. I have not researched it properly but it seems to me that Royal Artillery and Royal Engineers had no 2nd Lieutenants at that period, possibly becuse of their long professional training at the RMA Woolwich, they were commisssioned directly as Lieutenants. There did seem to be sub-Lieutenants with the Royal Sappers & Miners, although I have a note to say these were Sergeant-Majors who had been commissioned (ie promoted to officers), who would not therefore have attended the RMA.
As far as I can tell, most references to second lieutenant in the infantry (apart from Fusiliers or Rifles) at this period are to the appointment (not rank) of the second most senior lieutenant in the company. Confusingly, at a later stage, the rank originally known as ensign, cornet, sub-lieutenant or 2nd lieutenant (possibly the latter in Rifles and Fusiliers only) officially became 2nd Lieutenant in all regiments. Despite this official change certain regiments continued to refer to the rank of their most junior commissioned officers as ensigns or cornets (and some still do so to this day, just as the most junior soldiers, officially holding the rank of Private in every regiment, are known as Guardsmen, Troopers, Gunners, Sappers, Fusiliers etc). I stand to be corrected but, to the best of my knowledge, the British Army (unlike the American Army) has never used the rank 1st Lieutenant, always referring to this simply as Lieutenant.
The British Army has always been a loose confederation of semi-autonomous regiments, each with their own customs and terminology. The power of Regimental Colonels to decide on things such as uniform and military terminology within their regiments still exists today and was much more so in the Napoleonic era. As a result different regiments could use different terms to describe the same thing. This causes confusion to those looking for a universal description of the army at any period.