Though I am not in the military, I think the confusion maybe due to how the Army titles units. This creates units with similar numerical titles. Then factor in that as you stated , the numerical designators can get changed.These soldiers Unit (Brigade) are listed in the articles about them. I was reading about these soldiers and just happen to notice a lot are in the same Brigade or Unit (3rd Cavalry Regiment).
Units fall under Brigades. 3rd Cavalry Regiment used to be 3rd Armored Brigade (Same)
Going waaay back into military trivia....
US liaison officers with the British army in late WWII noticed that British "ordinary Tommy" conscript units had fewer desertions and creative malingering than US "ordinary Joe" conscript units. The Army then determined that for psychological and sociological reasons, the British Regimental System (BRS) created unusually tight bonds and duplicated some aspects of it.
So.....
US army units today can have confusing numbering systems. Battalions are usually placed in numbered Brigades of which most divisions have three (all numbered 1st, 2nd, 3rd), but battalions also have an honorific regimental historical association as well. Likewise, some battalions are call 'Squadrons' to maintain their historic Cavalry unit lineages (historic lineages are very important in the BRS).
The 3rd Brigade, 1st Cavalry division is a very separate unit from the 3 Armoured Cavalry Regiment. Likewise, as I'm Done mentioned, numerical designators can get changed when units are re-organized to reflect new missions.
Some changes are in part due to preserve historical lineages of famous units (3 "Brave Rifles" ACR). Thus, the units currently comprising the 3 ACR may have been in the 3rd Brigade of a Fort Hood division.
But... after re-organization, they have been assigned to the historic and now separate 3 ACR and took the regimental title and historical sub unit names (even more confusing is that the "Regiment" title of 3 ACR is actual, and not just honorific as with most regiments).
In short, units with similar numbers could have been can be totally separate in the past (two different divisions, each having a 3rd brigade). Likewise, they can still be totally separate today, even after the units belonging to a "3rd Brigade" were assigned the historical lineage colors of another unit such as 3rd ACR.
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