Well >I< get what you mean, but no one else will. No one is digging this deep into unofficial mongrels like us, so it's kind of the wild west for classification/categorisation and I guess it is reasonable for us to come up with our own sort of definitions.
Galgo patagonicos, which are a distinctive breed, are a little more than boergreys and most stags. Galgo pats are more on par with maritsane and wolfhounds. Many boergreys are really quite literally just greyhounds, but also get up to being like mid-range staghounds. Staghounds range from very close to normal greys to very close to GPs/maritsane/wolfhounds (or even equal).
So yeah it's all a bit vague and blurry, and it's gonna be tricky to draw clear lines and have clearly defined categories that don't melt into one another.
Fun to try, though.
"Greyhounds" in old latin were called "leporarius", from lepus meaning "hare". Which was better, really. More clear. Why they are called "greyhounds" is actually a bit of mystery, but the best explanation I have seen is "gre" or "gradus" meaning "first rank". Like they are the top class. And that works for us here, in a way. It's like the first level of sighthound are the hare-catchers.
But the confusing part is a greyhound IS serviceable on everything, all the way up. Hares, foxes, coyotes, deer, wolves, boars... in fact, even whippets are.
In a strange way it makes sense to have a dog "qualify" for the "next level up" when it can no longer consistently catch the main quarry of the previous "level". Instead of levelling up for gaining a skill, you almost have to level up for losing proficiency for the prey targeted by the lower level. It seems that's the best way it can actually work, and kind of how they used to do it. Mind you it does also come with enhanced ability for the next level, but drawing the line kind of works easiest with just going by when they can no longer catch the previous thing due to not being fast enough.
Like a sighthound almost becomes a wolfhound when it can no longer catch deer with consistency-
Biographical Sketches and Authentic Anecdotes of dogs (1829)So I think the first level is hare. Maybe also gazelles. Most sighthounds we talk about were not mixing with gazelle, but it seems to me the level of coursing excellence for hare and gazelle is pretty similar. Some lesser dogs might catch "a hare", but catching a european brown hare or desert jackrabbit or gazelles with a good success rate in a fair chase in the day time ... that's a very very exclusive club of dogs. Whippet, spanish greyhound, saluki, sloughi, english greyhound, kanni/chippiparai... I'd be ok with classifying these dogs as "
Greyhounds" or "Leporarius" or whatever. Maybe we need to come up with a better name.
The next level would be dogs who CAN'T catch hare and gazelle efficiently, but CAN catch fox and deer (including small fast deer) and coyote. Efficiently, again important to note. My bandog caught a fox, that doesn't count. In truth even a bully grey can't REALLY catch foxes consistently. Not by the standards of the "sporting gentleman" (maybe by wild predators standards). I'd be compelled to call these "
staghounds", also open to "deerhounds" (the latter problematic due to people thinking you mean scottish deerhound, perhaps, but we have the same problem with "greyhound"). The deerhound would be in this category, and staghounds. Maybe many UK lurchers.
The next level would be dogs that can catch wolves but not foxes and coyotes and small fast deer. Perhaps we could add some other semi-fast game in here. Warthogs perhaps. Maybe specifically large stags with no requirement for smaller faster roe and muntjac and axis deer, maybe wild donkeys and other feral equids. Etc. These are
wolfhounds to me. I consider the Galgo Patagonico in this category. Also the Maritsane.
The next level are
boarhounds. Now... remember, ALL the previous dogs CAN be used on boars, but "boarhounds" as a type should be dogs, IMO, who struggle to catch wolves and warthogs because they're not fast enough to do it with efficient consistency. They're not fast enough because they're burly bruisers ready for the WORST of the worst that wild boar can dish out.
Another level, even higher, is the
bulldog. Again so defined because it CAN'T run down and catch boars efficiently. Would be used as a "lead in catch dog" for boars. But can catch bovines (domestic or wild).
So I guess ultimately I'm not sure I do agree with your term. I'd actually put most boergreyhounds in the greyhound category. Staghounds of course in the staghound category. And GPs in the wolfhound category.