“Varmint” might be a derivative synonym to the modern form of its base word, but its documented use puts it twice as old as the United States of America… it’s a word with as much validity in usage as most words we use today.
Interestingly, in most of the Midwest states I have lived, folks seem to differentiate that “vermin” is plural, or maybe infinitive, suggesting a class of animals, whereas an individual animal would be a “varmint.” I’ve also noticed “varmints” often contains larger animals like coyotes and even hogs, whereas “vermin” typically draws the line at invasive small game, especially rodentia, skunks, opossums, frequently drawing the line even below coons. I’ve even had that conversation with Rick Paillet of Verminator (now Lucky Duck) Predator calls about the common perception that folks think his calls MAKE the sound of vermin, but he markets them as sounds to ATTRACT vermin - as in coyotes, fox, and bobcats. Neither are wrong, but colloquial use of the words favors a different definition than the owner’s intent.
In sporting arms, “Varmint” spent a lot of years describing any heavy barreled model, especially in short action. Notably, the comparison between the Rem 700 Sendero SF and VSSF - effectively the only difference was action length and associated cartridge chamberings, so two nearly identical rifles - one was dubbed a Varmint rifle, and the other a long range Easement rifle (the Spanish side sounds sexier, eh?)…
Way back, we saw “varmint” rifles being chambered in 308 largely for 3 reasons: 1) “varmints” loosely included “coyotes” which some folks believe deserve more bullet weight down range, 2) we didn’t have “long range precision” models or “target” models like we do now, so a lot of casual or even competitive long range shooters used “varmint” rifles (counting the casual “snipers” in here as well), and 3) it was rare to see any short action mode not offered in the 308. We didn’t start talking about “Predator” rifles until really around 2010, differentiated from “Varmint” rifles typically by features like a DBM, a more svelte stock profile, and a slightly lighter and often shorter barrel contour - and often with a faster twist. Which was about the same time we started seeing “Tactical” models like the 700 SPS Tactical, or Savage 10/110 LRT. We didn’t really see the “Precision” moniker introduced until 2015, again, commonly differentiated from “Varmint” rifles by twist, slight contour differences, maybe a DBM, and/or stock profile. So for a generation or two, heavy barreled factory rifles were “Varmint” rifles. Hell, when Remington introduced their R700 Police (predecessor to the PSS, Police Sniper System), it was simply an R700 VS - Varmint Synthetic - dropped into a new stock…
These days, it would be less common to see a Varmint model in 308 than in the past, as marketers have figured out how to better present those models as “Long Range Target” or “LR Precision,” or “predator,” or “tactical,” especially driving the idea that a consumer might need a “varmint” rifle in 223 with a “predator” rifle in 243win, and a “tactical” or “precision” rifle in 6.5 creed or 308win… and offering sufficiently different features in each to dissuade the consumer from thinking they’re just 3 copies of the same rifle…
So ~25yrs ago, if you wanted a heavy barreled factory rifle, or the barreled action therefrom, you were buying a “varmint” rifle.