Might help to understand a little more about the Security Police, before the Security Forces branding was created.
For many years, Security was split into TWO branches- SP & LE.
SP (Security) handled asset protection.
We wore standard OD fatigues, but with bloused boots, and worked as guards for planes, bombs, missiles, and other physical assets.
For the most part, we carried, depending on where stationed & type of duty, 16s, .38s, M60s, and so on.
Leather gear was a Bucheimer holster & dump boxes, worn on the old OD web belt.
Hats were ballcaps, till about 75-76, when the beanies took over.
Regular SP, to the best of my knowledge, never was issued or allowed to carry anything fancy on revolver grips.
We carried whatever was on the gun issued.
At a new base, you'd qualify with a .38 & a 16, you were given two laminated cards with "your" guns detailed on them.
Beginning of shift, before guardmount, you'd hand your card to the armorer through his window, he'd trade you "your" gun for it, and stick your card in the gun's slot on the rack to show at a glance where a checked-out gun was.
End of shift, clear the gun under NCO supervision at the clearing barrel, trade it with the armorer for your card.
You carried, unless something broke, the same two guns for your entire stay at that base. One shift might be a .38 at an ECP or indoor post, next shift might be an area foot patrol with a 16.
And they never went "home" to the barracks at the end of shift.
You took what was handed to you, and you did not dress it up.
In a combat zone, variations on the theme occurred, but this was the basic process for a working SP on an established base with on-base assets.
LE (law enforcement) wore some form of blues with actual leather gunbelts, typically a white hat, wore .38s (during my time in the 70s), did not generally do guard duty, aside from base entry gates, and performed some of the functions of a base police department in terms of patrol in cars (not trucks like SP), and handling problems like domestic disputes & so on in base housing.
Ongoing investigations of certain "crimes" were handled by an Investigations Unit, which could be plain clothes.
SP was the closest to infantry the Air Force had.
We were expected to detect, report, and repel attacks on a base or an asset.
LE was more of a PD, and not considered much of a part of base defense.
When we did drills & simulated exercises, I don't recall seeing them much involved.
Never saw them in restricted areas (nuke-loaded planes, other priority aircraft, bomb storage compounds).
Investigations handled thefts, drugs, etc.
The SAC Elite was a stand-alone unit ONLY at SAC's headquarters.
They had their own uniform, wore white scarves, blue beanies (long before the rest of us were forced to), their own duty belt, white boot laces, and those crossdraw holsters with stagged Smiths.
SAC Elite, being the palace guard, was very selective in who they'd let in.
You had to apply. If there was a vacancy, and if your record was gold-plated & you could present the appropriate SH appearance, you might have a chance.
Gotta look spiffy around all those generals & colonels & queens.
Denis