There are actually three belts: the ranger belt (trousers), the scout belt (money belt), the river belt (gunbelt). All use billets.
In historical order they are:
the scout belt, which you'll see in images of the Texas Rangers of the 1890s. Nelson's article about the Brill's origin actually has a specification for not only the holster, but for the scout belt: 6" wide, made of chrome leather, folded to 3" wide and stitched along the cut edge. Loops, usually rifle, are stitched before or after the belt is folded. No glue is used so that the belt can be used to carry valuables including money and bills of sale for such as the horse; a slot is at the buckle end for this.
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the ranger belt, which is a narrow trousers belt of 1-1/2" width or less, that is typically of unlined veg leather and has billets often of about 1". Its purpose may have been to give support for the holstered pistol while appearing to be just a trousers belt at the open coat. It was worn below the narrower trousers belt, which was not always through the loops because the pants did not originally have loops on them.
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the river belt, which today might even be called a Jordan belt, is a gunbelt of 2-1/4" width of veg leather with billets of 1-1/2" width; usually the river belt is lined. It was used as a 'western' substitute for a Sam Browne. I imaging that the 'river' was the Rio Grande :-). Today a Ranger would be expected to wear the classic ranger belt as the trousers belt, with the river belt just below it; mimicking the original arrangement of trouser belt and ranger belt.
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The Herrett's version for Jordan is atypical but LuckyB and I love it; the tongue billet is cut from the face of the belt, so it will lay very flat inside itself and allow the belt loop tunnel of Bill's Jordan holster to be very tight along the belt. Everyone else (LuckyB tells me these were made by Chet's) sews the tongue billet on top of the double thick belt, including Hume who was the 'preferred provider' of Jordan-marked products.
The 'attached thumbnail' is circa 1906 (the year he joined the Rangers) with Frank Hamer at left in his scout belt. The holster has been identified erroneously in Nelson's article as a Brill when it is instead its King Ranch predecessor (we have pics of the holster itself).