The DC+, DC-, and GND pins look to correspond. But NACS has 2 other pins. CCS1 has 4 other pins, and CCS2 has 6 other pins.
I assume there is some protocol on the other pins. A supercharger can read the car's VIN, for example. And some power/charge-state negotiation? Is all of this excluded from the NACS spec? Do CSS1 and NACS have compatible negotiation protocols?
The extra 2 pins on NACS are the ones that carry the CCS communications protocol. (CP and PP pins)
The CCS1 has the CCS communication pins, a big DC- and DC+ pin, and also three extra pins for AC slow charging (Line 1, Neutral or Line 2, and Protective Earth/communications ground). CCS2 has the DC pins, the communication pins, AC lines 1, 2, and 3, AC neutral, and protective earth/communications ground.
NACS has DC+, DC-, CP, PP, and a ground. Instead of sticking the bulky AC->DC converter in the car, NACS vehicles stick it in the charging station. That means an AC charger can't be as simple (it needs to convert to DC) but also that the car doesn't have to carry around something it only uses while charging.
NACS the DC+ and DC- pins are multi-purpose and can also support AC+/AC- (or, line1/line2. However you want to call it). There is absolutely no need to include a AC->DC converter in standard Level 2 chargers, and NACS does not do this.
NACS is slightly more complicated from a car perspective, as it requires the car to switch between DC and AC paths. There is literally no change from a charger perspective besides the handle, as chargers are not ever designed to be multi-purpose DC vs. AC.