Art,
The regimental system as you explained rose in the 1870s in the British Army, which had a large number of overseas commitments. Thus regiments were grouped on a two battalion basis, in some cases very much against their will. One battalion, on "war" establishment, would be out of the UK, while the other, on a "restricted" establishment, was stationed at home receiving and training recruits. As a rule, each year a draft was sent to the overseas battalion to bring it back up to strength. I think the battalions changed round every ten years or so, and overseas battalion could change stations every few years. It was very much the luck of the draw whether a battalion was sent to an overseas theatre where it could see action such as India, or to one where it simply garrisoned a colony, such as Bermuda,
There also were militia and territorial battalions, which could be identifed by their number. If my memory is correct, 3, and 4 were militia, while 5 and 6 were territorial, which came along after the Boer War. In wartime all this went by the wayside and as many battalions were formed as the market would bear.
To turn to the Canadian army, in the Great War numbered battalions were created, but these were eventually grouped into regional regiments, which were separate from the individual designations that might reflect affiliation with the militia regiment that spawned the battalion.
In the Second World War we had a number of battalions formed on mobilization in the Canadian Army Active Force. A militia regiment, say the 48th Highlanders, would be tasked to form a battalion of the active force. This new battalion was a separate entity from the militia battalion, and had no legal linkage despite being titled the 48th Highlanders. No one paid too much attention to that factoid and the members of both units as well as the press and the people at large considered them both to be parts of the regimental family. Other battalions of a regiment with both an active and a militia battalion could be formed for tasks such as home defence or the occupation force, and these might be the 3rd and 4th battalions.
In Canada, post-Korea we had six regiments, each of two battalions and a depot, except that the Vandoos had three and the Canadian Guards had four battalions (in the latter case for a short while). The Airborne Regiment came along in about 1967; rather than increase the manpower, the land forces went from 13 to 11 battalions, both the Canadian Guards and the Queen's Own Rifles dropped a battalion. In 1970 came a further reduction to ten battalions plus the airborne regiment. Each of the old permanent force regiments now had three battalions and a composite unit, 3 Mechanized Commando, was formed from members of 2 RCR and 2 PPCLI serving in Europe.
If one thing characterizes the Canadian army's approach to infantry organization it might be pragmatic opportunism, based in part on the realities of language and geography.
