That's not how people make threats. They are ambiguous for their own reasons. The media is supposed to report what's said, then people who know these things will tell what Putin actually means. The media jump the gun and put words in people's mounth is highly unethical, given the stake.
Deterrence isn't synonymous to nuclear why do I have to explain this. If you aim normal missiles to someone that's deterrence too.
Again, that is NOT the point here. The point is, the media's job is to report exactly what he said. "National Security", or whoever can then interpret it as "nuclear", and make a statement about it, then the media can report on that too. The media dubbing "nuclear" over what Putin said, is wrong. If we can't trust them on doing the basic job, then we can't trust them on anything.
“Deterrence” is not generally limited to nuclear deterrence, though there are contexts where that is implied.
One of the functions of the conventional forces being deployed to NATO’s eastern flank in the present crisis is deterrence, of the non-nuclear variety.
(Putin’s reference to “deterrent forces” given the context of recent highly publicized nuclear high alert and other circumstances pretty clearly implies strategic nuclear forces, but you are way overgeneralizing.)