OK, here is a pinout of the J1772 connector Note that it has two primary pins; L1 and L2, which we use to make 220V here in North America. The connector also contains a ground pin along with two small communications signal wires. If you use an adapter, like you mention, the L1 and the L2 which would be the other hot leg of a 220V supply or the neutral that would give you 120V. All Teslas have at least one built in battery charger. A single charger can supply up to 11.5 KW or 48 Amps. Such is fine for at home or parking space charging, where you are not pressed for time. The charging limit is capped at the max capacity of the built in charger in the Tesla. Supplying more Amps @ 220V has no bearing on how fast the car will charge. The difference between the J1772 and the NACS connector is that the two main pins in the NACS can accept high current DC and send it directly to the battery. Roughly 600 Amps @ 400 V, or 250 KW. The V3 Tesla Superchargers use a liquid cooled cable from charger to car. The communications pins in the NACS end are responsible for determining where the line pins connect, whether to the AC charger or direct to the battery pack. 
I suspect the reason you have never needed a DC charger has to do with the vehicle you are using. If you want to charge in 20 minutes, and hit the road, having added meaningful range, you need high current at high voltage, as supplied by a Tesla Supercharger feeding a NACS end.

(j1772 (full).jpg)

j1772 (full).jpg (44KB - 1 downloads)