It depends on what voltage you’re running it at, first of all. Then it depends on what you’re trying to do with it. If you’re trying to market the car, you’d probably use the Pmax value (and honestly, that’s probably perfectly reasonable because you don’t usually use the entire output of the motor for more than a few seconds at a time). If you’re looking for the maximum it can sustain constantly for 30 minutes (not super relevant in a car unless you’re doing something strange like towing up a very long hill, or maybe certain types of racing), then you’d use the second, smaller number.

I haven’t used the Tesla network (don’t have a Tesla, and they haven’t opened up to non-teslas yet), but their network really does seem to be significantly better. For one thing, supercharger stations pretty much universally have WAY more available stalls than anyone else’s. Anecdotally they seem to be more reliable, but even if they weren’t just the sheer number of stalls would make it less of a problem.

They also tend to be in more consistent locations, which makes them a lot easier to find. I’ve found CCS chargers in the corners of Walmart parking lots, tucked into alleys, stuck behind a gas station, inside a parking garage, and in a weird little spot behind an admitted very cute little museum of local history in a tiny town in Oregon. Supercharger stations are usually out in the open, are larger and more visually obvious from a distance, and are often either in their own lot, or are a significant chunk of an existing parking lot. I will say they don’t tend to be near anything interesting, but they are quite a bit easier to find than the somewhat hidden ones from other networks.

The biggest thing though is just how many of the damned things there are: Tesla’s Supercharger network is larger than every CCS network combined.

I don’t love their layout (few are pull-through, they don’t have card readers and rely entirely on an app/in car interface, and their super short cables are going to be a problem for most people who don’t drive Teslas, once that becomes a thing), but they undeniably have their shit figured out compared to any other charger “network.”

Pff, shale? Garbage rock, everybody knows chert is the real shit.

You’re not that far off; the alternator in an IC car is a device which converts a small portion of the power output by the engine into electricity to keep the 12v electrical system in the car charged up. That’s exactly what the generator in a series hybrid does; converts power from the engine into electricity.

The difference is one of scale; an alternator in an IC car only has to produce enough power to recharge the battery between starts, and run things like the headlights and the radio. In a series hybrid, that generator is taking all of the power produced by the engine and using it to either power the traction motors directly, or recharge the much larger, much higher voltage battery in the car. You can kinda think of it as a monstrous alternator (they mechanically work a little differently than an alternator, but they have a similar purpose).

In terms of what it is physically, it’s basically just a big electric motor bolted straight to the crankshaft of the engine. They’re usually a lot smaller than the traction motors when there’s a battery in the system, because you don’t actually use that much power on average in traffic. Think about it; when you’re accelerating up to speed you might use 50 or 60kW some of the time, but most of the time when you’re cruising along you’re using only 10 or 20kW. Because a series hybrid has a battery capable of delivering that big, occasional burst of power, the generator probably only needs to put out 30 or 40kW in order to keep the battery topped up.

There are exceptions to this, however. A diesel-electric train actually doesn’t have a battery (or at least not a big one); the output of the generator is used directly to power the traction motor. In that case, the generator ends up being as big as or even bigger than the traction motors, and in the case of a train can be pretty enormous. We’re talking many thousands of kW.

Edit: here’s another way to think about it. You know those gasoline generators you can use to power your house when the power goes out? If you put one of those in the trunk of an EV, you’ve technically made it into a series hybrid. In fact, that’s basically exactly what the “range extender” on a BMW i3 is; it’s a little gasoline generator. It doesn’t produce enough power to run the car, but it can (as the name suggests) increase the range by adding a little juice back into the battery as you drive.