The word "Pistol" is often used to describe any handgun and there are regions where the term is used almost exclusively to describe any handgun.
The earliest handguns were all pistols by current definition. A single shot, muzzle loading handgun that had a barrel with a chamber incorporated on the breach end would certainly be a pistol in today's world.
Flint lock handguns, wheel lock handguns and single barreled percussion handguns were all "pistols".
Pepper boxes and derringers complicated things a bit; but each barrel still had an integral chamber.
Revolvers, with one barrel but multiple chambers, were a significant departure from a pistol.
Tradition, language and regional influences play a big role in the terminology used. Spanish influence (such as places in or near Mexico) often cause any handgun to be referred to as a pistol (or Pistola
)
I understand the British use the word revolver and pistol interchangeably at times. The Germans use the words revolver and pistole to describe different handgun types.
The ATF classifies a revolver as a handgun with a single barrel, and multiple chambers arranged in a cylinder that rotates to bring each chamber in line with the barrel to fire. Now, ATF isn't the absolute authority on the matter but there is some basis for differentiating a revolver from a pistol.
As for what young verses old Texans call handguns, I will accept what you have taught me.