There's no wonder why Cavalry is a nebulous term in the US.
There is a distinction between the cavalry function and the titles of units.
For example, every BCT has a cavalry squadron (battalion) which perform reconnaissance and security functions as set out in FM 3-98
. Like all US battalion sized units each BCT squadron belongs to an "administrative" Regiment. For example, the 1st Cavalry Regiment now has its 1st Sqn as an armoured Cavalry Sqn with the 2 ABCT of 1st Armd Div while it's 2nd Sqn is the Recce and STA squadron of the 1st IBCT of 4th Inf Div. The 6th Cavalry Regiment provides Air Cavalry Squadrons to four separate divisional Combat Aviation Brigades.
On the other hand, several "Armoured Cavalry Regiments" have been converted to "Cavalry Regiments" (brigades) that are organized and equipped basically as Stryker BCTs (e.g. 2nd and 3rd Cavalry Regiments) or Abrams and Bradley equipped Armored BCTs (for example the Idaho ARNG 116th Cavalry BCT).
As such a given "cavalry squadron" can be anything from a Stryker battalion, a combined arms battalion or one of various different types of reconnaissance and security battalions including aviation units.
I think in discussing the term cavalry for Canada's purposes we are discussing what are in essence the reconnaissance regiments of the CMBG and comparing them to the cavalry squadron in an IBCT, SBCT or ABCT. Tactically and organizationally speaking we should be looking at their roles as set out in FM 3-98. What must be remembered, however, is the current difference in equipment as between Canada's Recce Regts and the BCT cavalry squadron. In particular, the addition of an Abrams tank company with the ABCT Cav Sqn and an Wpns Tp (of 12 MGS and 9 ATGM) with the SBCT Cav Sqn. The IBCT Cav Sqn is basically dismounted scouts or ones mounted in HMMWVs.
I'm not advocating adoption of their organization or doctrine but merely to look at them for research to see what direction Canada might wish to go. Similarly there is a lot to be learned from the deep strike concept in the UK. With what we're seeing in the Ukraine as to the use of ATGMs and GBAD there seems to be room for a more robust role for a properly equipped cavalry in the defence.