...Current Trip; Since Last Charge; Trip A; Trip B (a total of four settings in addition to the Odometer)...
Yes. They are 4 independent trips.
When your car was born, those 4 should be synchronized as 1 single number or very close.
Once, it's in your hand for the first drive, they start to have different numbers.
If you didn't reset the A, B, and "Since Last Charge" they should be all the same because the last charge was the first one from the factory and the numbers all start rolling from then.
That until you start to charge and the number "Since Last Charge" will diverge from A and B.
Does the car automatically reset to zero for a Current Trip?
Yes. it's for the current trip automatically.
Is it based upon Drive and Park?
It starts when you turn on your car and apply the brake pedal. It starts a new drive when you have to do that again turn on your car and apply the brake pedal. You might just park and stay in the car and will continue the same drive but the car might time out and you have to turn on your car and apply the brake pedal. To you, that's not a new drive because you were only resting in park but because the car timed out, it's a new drive because you have turn on your car and apply the brake pedal again.
So, if doing errands would it constantly reset when I stop and park?
That depends on your car status. If you stop and get out of the car, that's a new drive because you have to turn on your car and apply the brake pedal again.
If you stop and the car doesn't time out (the PRND automatically turns off when timed out), then it doesn't reset your number.
On Trip A & B, how does this correspond with the Current Trip setting?
See the first answer. They are all independent but they could be the same at some point like at birth, but after that, in some situation, they call can synchronize again:
You just charged your car. You reset both A and B. Now drive: All 4 of them will now have exact same numbers.