Of course. My dick is neither rifled, nor is it fired from the shoulder (juvenile braggadocio aside 
)
re: precision of language, try this on for size:
Commander: “…then when we hit the ridge, I want you to bring your guns around and enfilade the ravine”
Commander is thinking that he wants the unit that he’s directing to bring up their crew-served machine guns. If the person they’re talking to isn’t clear on the distinction, then they might just think the commander wants the unit to use their rifles, and as such bring insufficient firepower to the party.
Yes, any number of what-ifs can come out of that, but they’re all just permutations of a Spinal Tap skit. 18 inches? 18 feet? one tic, two tics? Who cares - they’ll know from context, right?
IME scenarios where distinctions like this are important are hard to dream up, but they happen in real life. During the post-analysis of a total clusterfuck, it’s very sad to realize that the root problem was a minor misunderstanding.
Do they carry around more than one type of gun on them typically? (Not sarcasm–generally curious. I get my military knowledge from Private Benjamin and GI Jane after all!)
Probably none. The object of the lesson is not so much to tech the recruits the difference between a rifle and a gun (rather significant, but besides the point) as to teach them to NOT be imprecise in their terminology.
A real historian can fill in some cites if you need them, but military history is replete with disastorous to catastrophic results of battles due to miscommunications resulting from hazy/imprecise terminology
Sidearms.
The term “handgun” is not used. You say “pistol” or “sidearm.” (There’s no need to refer to “revolvers,” because they’re no longer used by the U.S. military.)
“Shotguns” are referred to as “shotguns,” but I don’t believe they are very common on the battlefield. Shotguns are used on board ships and submarines, though. They are a useful weapon if you ever had to repel boarders in close quarters (which is most likely to occur in port in the modern era), and they are also used by the topside watches (i.e. guards) on a submarine in port.
I’m getting out of my expertise here, but I believe that “machine guns” are either referred to generally as a “machine gun,” or more specifically by the specific type of machine gun, such as the “SAW” (squad automatic weapon, a type of light machine gun) or a heavy machine gun such as the Browning M2. While a SAW can be carried by a single person, the M2 (colloquially referred to as the “fifty” or “fifty cal” due to the .50 caliber round it fires) weighs nearly 130 pounds including its tripod and needs a whole crew–you don’t want to confuse it with a mere rifle.
Note that shotguns and machine guns are not generally referred to simply as “guns” in my experience. A “gun” is a larger field or naval piece of artillery.
I’m not sure–I never served in the Army. I suspect it refers solely to artillery, though, similar to the Navy/Marine Corps, as in the “Guns of Navarone.”
Pistols are referred to as “pistols” or “sidearms.” They aren’t guns. 
Confused yet?
Don’t know how I missed this, but…
…with the caveat of “when I was in” (1986-1991 RA, 1991-1993 Reserves), “Gun” was indeed large towed or self-propelled crew-served ordnance.
Who knows what these young’uns are doing nowadays.
I was first confused when I heard the term “minigun”, which is basically a portable version of a gattling gun. At the time, I took it to be ironic, since they are obviously quite large compared to a regular sidearm.
It’s called a “minigun” because it’s a smaller version of this weapon (the M61 Vulcan, a 20 mm six-barrelled Gatling-type rotary cannon), and a much smaller version of this monstrosity (the GAU-8/A Avenger, a 30 mm seven-barrelled Gatling-type rotary cannon). This classic photo gives a sense of the size of the latter weapon.
It’s more of a point of laying down the fundamentals. While the consequences of calling a rifle a gun may be minor, it’s important to use accurate terminology in a combat situation. This is just a minor reinforcement of that.
Everything on the radio has an appropriate transmission order. The making of a distinction between a gun and a rifle in Boot is a way of instilling in recruits that when the time comes you need to use the official methods.
This was my take on it too. It’s basic training, and they are training you that there are 2 ways to do things: the way you are told and the wrong way. It’s true that mixing up “rifle” and “gun” in the field probably wouldn’t have life or death implications, but other mix-ups might, and you are not in position to to decide which rules, regulations, traditions, and policies can safely be ignored. Therefore, focusing on the seemingly insignificant difference between “rifle” and “gun” to the extreme that they do drives home the point that you will follow orders to the dot, not sit back and question whether the orders are sensible or significant.
“Captain, we’ve encoutered enemy forces, taking gun fire”
“GUNS ? Holy crap, we’re not equipped for that. Pull out, I’ll call an air strike”
“Aye Cap’n. aside See, Mac ? All officers is pussies, we could totally nail those 2 dudes with AKs…”