That's correct - unless the nomenclature has changed in the last decade the term for a rifle in the British army is "individual weapon", as in used by one man, then you have "Light Support weapon" which is the minime these days, and a bayonet is a hand-to-hand weapon.
In the UK "gun" refers to heavy support like machine guns and artillery that need more than one man to operate.
Which, of course, doesn't stop swaddies from referring to anything they can hold that goes "bang" as a "Gat"
The term "firearm" in the UK is not in common usage at the moment, but when it is it can include everything from fowling pieces up to mortars.
Regardless, to have a firearm is to be equipped with a weapon - if there's a nuance here it would be that "firearm" implies the intention to use it for violence while "weapon" only implies potential for violence.
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