OK, it's like this.
First, there's the Actual Battery Charger. It accepts DC, does a DC->DC conversion where the output goes into the actual batteries.
Then, there's the rectifiers. These accept AC, either at 120 VAC or 240 AC (in the states: In the EU, they got three-phase), converts that to a DC voltage, runs it through another DC-DC converter, with the final DC available for the Actual Battery Charger.
Then: the Actual Battery Charger can accept a DC voltage from one of two places: Direct from the plug at a Supercharger or from the output of the rectifiers.
Interesting factoids:
- DC->DC converters are, relatively speaking, cheap and highly efficient. They take in a DC voltage and, with a certain number of big, fat switching transistors, run current first one way through the primary of a transformer, then the other way through the primary of a transformer. This is done at a switching rate as high as the market will bear, somewhere (typically) north of 700 kHz, and I've heard of ones running as high as 10 MHz. The switching back and forth is pulse-width modulated and is controlled to set the output (secondary) side of the transformer output voltage.
- Why the high frequencies? Because transformers are made out of inductors; the reactance of the windings of a transformer is what makes a transformer go; and the reactance is 2*pi*f*L, so (a) one gets to use smaller inductors as the frequency goes up and (b) small inductors tend to have less losses than big ones.
- Then, consider the rectifiers. Input frequency: 60 Hz (50 Hz in the EU). The lower in frequency one goes, the larger the various inductors and capacitors required to filter the stuff to a reasonable DC value get. It's almost trivial to filter a 1 MHz 10 kW power line; trying to filter a 60 Hz 10 kW line means Extra Big Capacitors that are expensive, take up a lot of room, and, technically, have loss factors and heating issues that smaller capacitors don't have to contend with.
Next: Why 32A at 240 VAC? Well, that's about cost. My understanding is that there are two or three rectifiers in a Tesla these days. Each rectifier can do 16A and costs $$. Now, say one has a M3 LR or P: Comes with a 75 kW-hr or so battery. A full charge, starting from zero, with 240 VAC @ 48A = 11.52 kW is going to take 75 kW-hr/11.52 kW = 6.5 hours, using a Wall Connector and all three rectifiers.
Now, take a SR. It has a smaller battery. Checking on-line.. 60 kW-hr. Suppose this car has two rectifiers (which they do), so one gets 240 VAC @ 32A = 7.68 kW, which, for a starting-from-empty charge time of 60 kW-hr/7.68 kW = 7.9 hours.
Point is: That's also overnight. And it makes for a cheaper car, with two rectifiers rather than three, just like the smaller battery makes it cheaper. So, they size the rectifiers to match the battery size to save the customer some $$$.
Finally: As pointed out above, the charge rate at DC Superchargers isn't affected. You can still get 250 kW at a SC into a Tesla SR (at least, for a short while, while the battery's mostly discharged) just like the LR and P guys do, so it should take a little shorter time for an SR to get in and out than a P or LR.
Questions? Ask 'em, we got answers