The Nonmen operate under some kind of Caste system. Somewhere near the top are the Ishroi. The Ishroi are described as the warrior-caste, and I suppose this affords them a place of honor in their system.
The Quya are the magi of the Nonman society. I don't think Quya is a caste, more like a title given to those with the power to wield magic. The Quya could be Ishroi or any other caste. For example if a schoolman was also a caste-noble he'd be called a Kijneta Schooman. I think the Nonman would work under the same principle, meaning that you could have a Quya Ishroi, or any variation of Quya [insert class name]. To my knowledge, we only have been told of the Ishroi caste (unless you count Emwama).
A Quya may be an Ishroi as well, but an non-magic Ishroi can never be a Quya.
You were pretty much right though: Ishroi are the non-sorcerous warriors, while Quya wield magic.