Offhand vs Off hand
I always thought offhand was with one hand. Either left or right, strong or weak. Like an offhand remark. Not quite snap shooting, but not bullseye slow fire from a bench, either.
On the other hand, when I see off hand as two words, it means from the other side, or non-dominant or "weak" side. The concept of "off" as an adjective has implied association with the naval term "to stand off", or away from, meaning the side not close to your point of reference. Also kind of related to the football term, "offsides".
Semantics. If you think "being close only counts in horseshoes and hand grenades", you haven't studied the Englsh language much. The language is maddeningly vague with misinterpretations abunch. Why do you think lawyers are so highly paid? As wordsmiths, they spend a LOT of time defining terms.
So, in competitive shooting, "offhand" will mean what the rulebook says for whatever type of competition and governing body says. And that may be totally different in one venue or another.
This is the long way of saying, there is no definition until any given conversation agrees on a definition. I have seen (and been in) a lot of arguments wherein both sides are actually in agreement, except they don't agree on the terms and therein lies the rub. They don't even know what is is they are arguing about.
Lost Sheep.