I have no background in psychology but... is conditioned reflex even a valid psychological term?

Many human cognitive abilities are unconscious, like, in most cases, face recognition, so while I am not typically doing deliberate conscious mental math when distinguishing between my mother's face and my drinking buddy's face, it doesn't make sense to call it a "conditioned reflex" either, it seems to me. My brain is doing some sort of thought that I am not consciously aware of. That doesn't mean thought isn't happening.