Aw Red is so cute! I love how Doctor and Kal'tsit have different perspectives towards the adorable Red, wait hold on... Why did I level up Red so much then put her in the base all the time?
To the old Doctor, those killcount is just a baby's compared to his. And he DID know that Red was working as an assassin, it's just his old man filter can't help but see her as a kid given the difference in age and experience.
There's also the possibility that Gwenpa added more experience to this pup's skills by sparring with her or going full ghost that not even she can sense
I think Red says CS is more like a primordial wolf than a true wolf
CS is a Lupo but not a "Wolf". Much like how Lappland and Texas wouldn't be "Wolves". The term is used to denote Lupo that were trained by one of the strongest Lupos.
Red killed CS's master because they were a traget in the killing game that all "Wolves" are being forced into. Lunacub is a "Wolf" herself though there was arrangements made by Kal'tsit between Red's and Lunacub's masters so the two didn't have to fight to the death. We don't know if it is a truce or if it involved Lunacub being made to forfeit.
Red tells CS that she isn't a "Wolf" and will never be a true "Wolf".