Haha All good questions... I'll do my best...
First, the older doubler method results in a no load voltage of about 320V across the caps, which dips quite a bit under heavy load, just as any unregulated supply does, only worse because of the "half wave nature" of a doubler fed by sine.
In active PFC, the 380V point however is a set point (regulated), and is typically chosen to be above the older doubler scheme, but presumably only by the necessary amount to accommodate the nature of boost converters, as this would make the PFC more or less a "drop in" replacement for the doublers in tried and true designs (which is exactly what happened in this case). If someone knows something to the contrary, by all means, as that's just speculation on my end.
The exact voltage isn't critical when it's used in this way, provided the MOSFETs used both for the boost converter and the main converter that follows are adequately rated/snubbed. It's usually in the 360-380 range (the charger actually reads something like 376V or so, sagging only slightly under load, down to around 372-374). Many times, the reservoir caps used (electrolytic) are rated for 400WV, so it will of course be below this.
The margin above 320 is to accommodate the 240V mains countries, without needing to manually select the voltage with a physical switch like on the old supplies. A boost circuit is not capable of producing a regulated output that is a lower voltage than it's input, because the DC path from input to output has no switching components in series in between (only an inductor separates them). To accomplish high PFC, it must always be regulating, so the target voltage is set higher than the peak AC voltage would normally reach (240 * 1.404 = 336.96V). Why is it called "320"? Nominal? Anyone? LOL Anyhow...
The boost converter is set up slightly differently for PFC than for typical DC usage, but for the most part, this is mostly at the cap used at the input. Instead of a relatively large electrolytic or tantalum, usually a much smaller value metal film cap of some variety is found in its place, immediately following the mains rectifier bridge. This is because it needs to be able to track the 100/120Hz rectified sine rather closely for the PFC to reach as close to unity PF as possible. Ideally, for phase distortion considerations (which counteract the active PFC with capacitance on an otherwise "resistive" load), it wouldn't be there at all, but the boost topology needs it to work correctly.
To accomplish the PFC, the boost converter more or less functions just like it's DC counterparts that you're (hopefully) already familiar with. It targets an output voltage, varying it's PWM as required to maintain regulation, as the input voltage rises and falls over the rectified sine, and load on the output changes. The overall pattern this results in is near maximum duty at the beginning and end of each sine pulse, with the lowest duty being seen at the crests of the waves. Load at the output causes the overall duty percentages to increase, with most of the difference being seen toward the crests.
The result is the entire wave produces output power, and not just the crests as in the doubler scheme. The loading effects this has, as I'll get to next... In a nutshell, the upstream source doesn't experience the disturbances that cause distortion of the sine.
Why is this important? Well, the problems that a simple doubler scheme cause are a little bit different in part from the voltage/current phase issues seen by things like directly mains powered transformers and motors... the main difference being that it introduces wild harmonics back into the source, that can't be controlled and compensated for by legacy L/C correction schemes. This is largely a "grid phenomenon" (meaning it is easier to "overlook" on smaller scales such as local generator feeds and the like). As SMPS gained popularity and presence on the grid, the distortions increased, and began posing problems to the infrastructure that again, passive PFC (within the grid) could not correct.
The other issue it causes, while different in originating nature, has the same end result - increased need for peak current handling. With SMPS (or countless, dozens at least) in every house on the planet pulling hard peaks at the crest of each wave, the impact on the grid is non-trivial. This is the more "visible" issue, in that the effects scale from single unit to the millions, with an even greater effect than the harmonics...
Let's take an SMPS that draws 1000W (for round number purposes) and ignore efficiency considerations for this example to keep the math cleaner, as it's a completely different concept.
It only *needs* 8.3A at 120V in doubler mode (or 4.15A at 240V in full bridge mode), but can, at the crest of the waves, draw current on the order of multiples of those during the peaks. Double, triple, quadruple even, and up. So let's play right down the middle and say the current spikes are hitting 3x average power used by the load... and rile the chip up... 1kW *average* power going in, 1kW coming out... but that's not what the upstream source needs to be capable of; it's seeing the need to provide a 3kW spike, even if only for a brief moment every cycle.
It is this spike of current multiplied by the instantaneous voltage within the "window" at the crest that becomes your "apparent power", and the upstream source, whether it be grid, generator, or inverter, must be able to provide it while it's being drawn in order for the SMPS to feed it's load.
With PFC, the entire wave is supplying current to meet the actual power requirements of the load on the other side of the SMPS, the effective result is that the upstream source sees a mimicked resistive load, which has a perfect theoretical power factor (translates over to 100% "real power").
The harmonic distortion and behavior of the current spike are interdependent, in that the harmonic distortions induced in the upstream source are a result of the impedance of this source, and the distortions lead to further complexities that manifest as further disturbances in the current spikes, that result from the crests of the waves changing position, amplitude, and duration.
In the case of a smaller scale system, while the distortions still exist, the "round robin impact" is somewhat subdued, as the peak current demands can become the dominant problematic issue (by tripping fast acting overload protection schemes such as hiccup) before the distortions can cause problems, but not always. This is largely dependent on what types of other loads are also present within the system, and the impedance of the source. Generally speaking however, the main point is that "the grid will just keep on giving until something pops, and they'll just bill you for it, your generator and inverter will not".
(Ok, so generators and inverters can pop too, but that kind of popping is a massive PITA to "reset", and can come with a hefty "bill" of its own)
Hopefully, I've answered your questions with this, and didn't just add more confusion lol...
Steve