That line, "take specific action to reload", is the same follow the fiction / the fiction decides as anything.
What it does is differentiate weapons where we don't care about when the reload happens and the ones where we do. With any handgun that doesn't have the reload tag, you just keep shooting during an action scene and if it's even remotely possible that you have enough bullets and time to shove them in, that's just assumed to happen. I mean, you can always construct extreme cases like "I stand overwatch, shooting a steady one round per second, from now until forever", obvs the lack of a reload tag isn't going to keep the MC from having you reload at some point. Same thing as selling infinite knives one by one.
What the "specific action" line gets at is that for those weapons, after using it the player actually has to describe how they reload the weapon. Not in detail, but state that reloading is what they do. If they have the ammo, and have time and safety to do it, that's all there is to it. But the act of stating that at the table means it's something people think about. The player is incentivised to plan their violence so that it allows them that time and safety to reload; so for example, to drive out a whole gang, with an ak47 you can start shooting in their midst but with a shotgun you'd prefer to be behind cover for some up-shoot-down-reload. The MC is prompted to think about what happens during the reload—and again, if it's short and well-planned, maybe the answer is "nothing, it's damn quick". But maybe someone hears it. Maybe an inexperienced character fumbles with the shells, and that means when they pop up, Machete Millions is closer than you thought. Everyone is reminded that yeah, their ammo stores actually dwindles with every combat.
In contrast, non-reload weapons only require ammo inasmuch as the MC and players actively remember to think of it. Otherwise they sort of operate by action movie logic.
The autofire tag is interesting: if you take out people one by one, no-one cares about exactly when one magazine ends and you start on the next one. But lay down sustained fire to get the 'area' effect, and without fail, you're shooting 'til it starts clicking, no more, no less. There is no way in AW to empty the whole mag except for one bullet. After using autofire, the explicitly described fiction (as implied to the fuzzier implied shared fiction) must include that weapon being reloaded if it's to be used again.
So yeah, to repeat Daniel Wood's observation: it doesn't say "take an action" because actions aren't formalised like in DnD where you get X of them each turn. Instead, it says "take action" because it requires you to take action. And to do it, do it.