On the Model S, Tesla has different torque limits for different S models. This determines power for the first two seconds. Then the battery output determines power for the next several seconds. Then the physical motor constraints at various rpm levels, influenced a little by battery amperage, determine the high speed power.
The model 3 RWD behaves the same way. The biggest difference being that the motor constraints happen much earlier, right after peak power. Another way of thinking about this is that the Model S motors have more low end headroom for future bigger batteries, and that the 3 RWD is more evenly balanced.
We don't have good data on the 3 AWD or P variants yet.