Do you compete with the same gun you carry (or essentially the same gun)?
This primarily considers IDPA competition since USPSA has become so dominated by customized pistols and sights. (you are not likely to carry around one).
Do you carry the same gun you compete with, or the same make/model or something substantially the same?
I don't think carrying a Glock 17 and competing with a 34 is substantially the same.
But Shooting a Cz75Shadow for competition and carrying a Cz75B might be substantially the same.
The debate came up in an experimental Action Pistol competition where they are trying to rewrite a better game than IDPA, and they excluded all guns with barrels longer than 5" because they want to keep the competition to a class used truly for CCW.