I am not very expert in this confusing subject but I do know that one factor in different British regimental establishments was the Irish situation.
The British Army was, and still is, a collection of regiments each with a fiercely tribal ethos, thinking they are better than everyone else and seeking to perpetuate their existance. The senior officers of the British Army, then and now, have risen from that background and, on the whole, wish to perpetuate that system, often acting as lobbyists for their own particular regiments. This surfaces whenever there are proposals to disband or amalgamate regiments. The regiments today may be on a common establishment but have many variations of custom and dress which are fiercely preserved.
The army owes it loyalty to the monarch, but its funding is voted by Parliament, this separation of powers dating from the restoration of Charles II after the English Civil War. Until comparatively recently (within the last 20 to 30 years) Parliament had to pass an act every year in order to fund the armed forces, and without which they had no legal authority to exist. The idea being that if the monarch dissolved Parliament then, by default, the armed forces would cease to exist within the year, thus making it difficult for a King to use his army against Parliament.
In the 18th century, as now, Parliament funding for the armed forces in peacetime was a constant attempt for economy. There was therefore a conflict between this and the vested interests of the army hierachy in keeping as many regiments in existance as possible.
One way the generals solved this was to exploit the different funding arrangements within the United Kingdom. The British Government in London only controlled the funding, and thence establishments, of those army regiments based in England, Scotland and Wales. Those in Ireland were separately funded (and therefore their establishments set) by the Irish administration. The generals therefore arranged to have relatively large numbers of regiments, each of low strength (effectively "cadre" units) shown on the Irish establishment. This saved them from disbandment or amalgamation. It also of course gave a much better base for expansion in wartime so there was quite a lot of military sense behind the system.
All the regiments belonged to the same numerical series and there was no logic I can see as to which regiments were in Ireland on low strength and which were in mainland Britain on higher strengths. Rotation (ie movement between bases) did take place from time to time.
This was the starting point from which different establishments emerged. As troops were dispatched overseas they would be brought up to a higher establishment which could vary depending on whether they originally came from the mainland or Ireland. At various times during the Revolutionary and Napoleonic wars Parliament authorised increases in regimental establishments and formation of second or even third battalions. These all affected official established strengths but if the regiment was by then serving overseas it took some time for changes to be implemented. This latter factor is common to many armies (ie French battalions in Spain still operating on 9 companies per battalion after the change to 6 companies had been implemented back in France).
I am sure there must be an article on this in the Society for Army Historical Research Journals. My copies go back 30 years so I will have a look.