If a Canadian resident (who is not a citizen of Canada) applies for the NEXUS card and is subsequently refused for some reason, would that refusal count as a visa refusal? Technically speaking NEXUS is not a visa, but at the same time it is issued by immigration authorities and can act as a replacement for passports at border crossings.
No. If asked a question that specifically asks if you've been declined admission into a trusted traveler program, you'd have to answer "yes", but NEXUS and other trusted traveler programs aren't visas, so you haven't been declined one.
NEXUS gets you lighter treatment at the border, but has nothing to do with whether you can enter or not. It just means you're considered to be lower risk, so there may be fewer questions asked of you. (I've had this confirmed by Canadian border agents.) You tend to be given the benefit of the doubt more, but if there is doubt, you can and still will be asked more questions and even taken to secondary inspection, so it has nothing to do with your admissibility, except that if you're clearly inadmissible, you'll be declined admission to the program. Plenty of relatively low-risk travelers are declined NEXUS, and it affects their ability to cross the border not at all.