Really wasn't my intention to get into a war about what Qunari means as a race. My intention was to sort out the importance of the Qunari PC being Vashoth and what it means for mages. As far as I knew, there was no evidence that Tal'vashoth and Vashoth were inherently exclusive to the race itself(Vashoth itself in the codex entry link I posted is simply explained as someone born into the faith who then rejects it), but apparently they must be. This line of reasoning makes a Vashoth-born Qunari PC make sense, which is fine, but I think the terms aren't as clear as they should be.
They are purposefully made unclear. The three idiots governing that religion believe there is no importance in biological classification of creatures. They only refer to themselves as Qunari as they are the ones following the Qun and that is all anyone needs to know, according to them. But now, they have escapees and rebels who call themselves Tal-Vashoth. These are the ones that do not follow the Qun but also only care about killing whoever they see and take what they have. Vashoth are the ones who are either born outside of the Qunari society or have escaped from it but only wish to live their lives, not wreak chaos like the Tal-Vashoth. This is what I got after reading some dev quotes.
Kossith is used by some of us as the race's biological identifier rather than Qunari. I use it because it is antiquated(hence barely ever used) and also because it makes it easy to to denote to the race when compared to the word Qunari. "Iron Bull is Kossith but I don't think he's Qunari". As for the Mages, call them Kossith mages if you like. In the game however, you will hear a lot of people calling you Qunari, Qunari Mage and as Saarebas.