The thing is that Hellfire is a very specific power in the DF where you draw from the Fallen's Hell.
I can buy a functionally similar sponsored magic being provided, but even if you take them as all being the same tier they wouldn't be the same thing and wouldn't be referred to by the same name by someone like McCoy.
In part it's a cultural branding thing. No American is ever going to call a burger a grilled beef sandwich even if that's technically accurate description. Similarly, a burger made with other meat will get called out. A turkey burger will almost always be called that instead of just a burger.
If he meant Lanka's hatefire or something then he almost certainly would have been specific.
This.
When he first met and talked with Molly, he described her not as a hell-princess, but specifically as something out of Lanka:
"Dad I literally felt absolutely nothing," you insist squeezing his hand to make the point that you are alright, other than being an icicle and all.
"OK so we have established that Outsiders cannot mess with my head and they burn when I set them on fire..."
"Usually when something looks too good to be true that's because it is," McCoy cuts you off before taking a sip of his coffee as if daring you to argue. "Lucky for you that you look like some mad conjuror's set loose one of Ravana's Maharajas until we had a sit down. Good talk."
Usum actually starts giggling. "I like this one."
This was after seeing Molly's hell aura and demon sword with all the fire on it.
When he says Hellfire here, he isnt likely to be talking about something out of the Thousand Hells.
Or from beyond the Outer Gates.
Dude has the experience to be precise about what he's referring to.
And precision is probably necessary here, since he's about to lead other wizards into combat.
The vulnerabilities, and applicable banes, of the hostiles they will meet are different depending on their affiliation.
Holy water might work on people aligned with Hell; wont work on Outsiders AFAIK.
They even source them to other factions/individuals like the Walker we fought at the ball. Kind of undermines Winter's efforts at the Gates if a global scale faction blatantly brings them in past the Gates and furthers their agenda. I wouldn't be surprised if Peabody was sourced his current patron from the Reds it's that bad.
We know nothing about the source of the Raith Ball Walker.
The White Court has its own independent history of meddlers playing footsie with Outsiders; the White King has an antimagic Investment from Outsiders, and was using an Outsider-summoning ritual to kill people in Blood Rites.
There is no grand conspiracy of evil, and Evil will backstab Evil as soon as they find it profitable to do so.
Do remember that the White Court under Lord Raith masterminded the fall of the Black Court of vampires.
And in this quest, the Red Court specifically fucked over Iku-Turso and the Pathfinders.
They act in their own perceived interest.