”Wearing” a gun pretty specifically is used for having it in, or at least with, a holster (I’ve seen it used a lot, and always with that meaning; it is pretty much the combination of wearing the holster and carrying the gun that goes in it; I’ve mostly seen it used of people who do that regularly as part of a job or lifestyle, either speaking about them in general or discussing whether they were or were not doing so at a particular time.) “Carrying” is more general and more often of interest.
> Don't cops ask "Do you have a gun on you" or "Are you carrying?"
In person, I’be most frequently observed the former (fortunately, not much experience), but on TV both cops and crooks tend to use “carrying” with an implied direct object a lot.
> I think most of us would find it weird if a cop asked us "Are you wearing a gun?".
Sure, because that's not what a cop is likely concerned about.
> Don't cops ask "Do you have a gun on you" or "Are you carrying?"
In person, I’be most frequently observed the former (fortunately, not much experience), but on TV both cops and crooks tend to use “carrying” with an implied direct object a lot.
> I think most of us would find it weird if a cop asked us "Are you wearing a gun?".
Sure, because that's not what a cop is likely concerned about.