By the way, in the 31st Century AD, they solved the problem with machinegun-barrels overheating; MGs produce zero heat.
It's all about timescale. By the book, a machine gun firing 100 rpm in 6-9 round bursts wouldn't need to think about a barrel change for ten minutes. I personally have never seen a BattleTech game--even battalion level engagements of which I have participated in several in my heyday of the early-mid 90s--go for sixty turns with MGs firing continuously. Now, an old-school
Solaris VII dueling-rules fight might be getting close to overheating a real-world machine gun (firing a burst or more every 2.5 seconds) could change things. But then
MLO4H is onto something.
Maybe those "battalion of
Stingers versus an
Atlas" fights we always hear about apply here...

EDIT:
Of course they do. They weigh 500 kilos! They're going to shoot out the rifling of those barrels long before they run out of thermal capacity of that much liquid coolant.
And there is that, too.
So is there a difference in doctrinal usage for a machine gun when it's being used by an infantry squad vs a vehicle? I played D&D wit a guy a long time ago who'd talk about being a door gunner on a UH-60 and stuff they'd do on training (I'm pretty sure he never actually saw action). Liked to brag about how he and other guys would hold competitions to do things like see who could cut a tree down faster.
Never underestimate training. If it wasn't important, even vital, the US military wouldn't place such emphasis on its Training Centers. But sure, some real-world experience puts some needed tempering on it. Having said all that, I do find that many other veterans' claims of their training does not square with my own. For me, training was focused and directed--even the free-form actions at NTC and JRTC--with little opportunity for nominal "horse-play" (or less charitable terms like "F-F games") like cutting down trees with airborne machine guns.
I mean, there are things like range-safety officers and NCOs watching everything you do. But hey, not every unit or station is the same.
Doctrinally, I suppose the differences between a grounded squad machine gun and aerial machine gun could be either zero or a hundred. Technically, the weapon itself is a little different between the pistol-grip/buttstock of the infantry M240B and the double-spade grip of the M240H (but they make an "egress kit" to convert the -H into a -B for dismounted operations). For what it is worth, the reference you are looking for is Appendix A of FM 3-04.140 (newer version of FM 1-140) Helicopter Gunnery. I spent a lot of time on helicopters of various types (mainly -60s, but also vismodded UH-1s at NTC), but was never a door-gunner nor even fired out of a helo.
Some differences between ground- and door-gunners are the fact that the door gunner doesn't have many of the aids the ground gunner has regarding range to target, the firing platform is normally moving, and they do not have a leader or assistant to help monitor ammo usage, firing patterns, etc. Whatever they do, they do on their own. Sure, they have an aircraft commander involved, but not like an infantry squad or platoon leader/sergeant.
The root of the difference is that the infantry MMG is designed to assist the infantry squad and platoon accomplish its mission, whereas the helicopter MMG is for protection of the aircraft. FM 3-22.68 tells us:
The M240B machine gun supports the rifleman in both offensive and
defensive operations. The M240B provides the heavy volume of close and
continuous fire needed to accomplish the mission. The M240B is used to
engage targets beyond the range of individual weapons, with controlled
and accurate fire. The long-range, close defensive, and final protective
fires delivered by the M240B form an integral part of a unit’s defensive
fires.
The M240H in a helicopter door-gun mount is actually used to hit close(r) in targets that are relatively clearly visible to either protect the helo itself, or suppress likely engagement areas preparatory to landing to unloading/loading personnel or gear*. Door gunners also have fields of fire they are responsible for, and these change depending on how many helicopters are operating together, and which side of the aircraft they are on. That in itself is a paradigmatic change from an infantry gun-team, which is controlled by a platoon-level leader and has...whatever sector of fire is assigned to it at the moment.
He liked to tell a lot of stories about doing stuff, if you get my drift.
I knew a gentleman who did two tours in Vietnam, much of it as a door gunner on a Huey and possibly on a Loach. He didn't tell any stories. I get your drift perfectly.
*Movies make it seem like door gunners are doing all that firing to support the troopies unassing the helo. Really, they are doing to prevent themselves from getting shot up. I don't begrudge them that. Because I wanted them to leave safely so they could come get us all later!