I think the short answer is the naming of military units is often the results of a long and possibly convoluted history, reorgs, renaming, renumbering, and restructuring.
Further complicating things is that some units are “administrative” units while others are actual combat formations.
For example, a “division”, like the US 10th Mountain Division, consists of roughly 10,000 to 20,000 personal and all their equipment and vehicles.
There aren’t 9 other “Mountain Divisions”. It was originally formed as a “light infantry” division and at some point renamed to signify it’s special mission fighting in areas of rough terrain.
The division is organized into 3 “Brigade Combat Teams” (several thousand soldiers) along with a headquarters, aviation brigade, artillery, and a support brigade.
Each brigade has a bunch of battalions.
If you notice, each battalion has a name like “1st battalion, 14th Infantry Regiment”.. In the US Army, regiments are administrative units, not combat formations. That means the regiment’s three battalions (1st, 2nd, 3rd, and 5th (@Dissonance - You’re right…no 4th/14th Infantry) share a same history, unit insignia and whatnot, but each battalion might be assigned to a completely different division.
You might also notice that the 14th Infantry Regiment was created during the civil war, but was subsequently reorganized and often reconstituted as different size units (ie battalion instead of a regiment).
As I understand it, the main reason for doing this is to create a sort of shared history and esprit de corps at the unit level for similar combat arms (ie “armor”, “infantry”, “artillery”, etc). But in practice, actual combat formations consist of “combined arms” of tanks, infantry, helicopters, and whatnot all working together. Like they don’t send a whole brigade of nothing but tanks into battle. The army deploys a more flexible “Brigade Combat Team” consisting of maybe a tank battalion, several mechanized infantry battalions, and other supporting units.