Cat, now you are talking!

I think I can help you understand the Smart System, as these concepts are similar (but not identical) to what Specialized does.
General concept
The mid-drive motor system measures your leg power = torque * cadence and translates it into the motor power delivery (I will always talk about the mechanical -- not electrical -- values). I will only talk about the regular modes: ECO, TOUR, SPRINT, TURBO.
Assistance
Your measured leg power input is translated into the power demand from the motor. It is what I call Boost or Amplification.
Let us assume you are in the
preset called SPRINT, and that preset is set to 280%. Let us also assume your current leg power input is 100 W. A request is created so the motor would provide 100 * 2.8 = 280 W mechanical power
if this is possible based on other parameters.
Max Power
This is an artificial cap on the motor power delivery. If a rider is a strong person and the Assistance is high, the motor output power can be capped to avoid premature battery discharge. In the previous example, the motor power request was 280 W. However, the rider could try pedalling harder and delivered as much as 150 W with their legs. The assistance request would be 150 * 2.8 = 420 W. If the Max Power is set to 250 W then the motor will never deliver more than 250 W
, disregarding how strongly the cyclist is pedalling.
This is the single parameter the most affecting the battery economy.
What is tricky here is Bosch seems to define the Max Power by Max Motor Torque. You need to understand that the actual motor power is Motor Torque * 6.28 rad/s. Therefore, let us calculate the Max Torque to be set for 250 W motor power cap: 250 / 6.28 = 39.8 Nm. So, if it is set at 40 Nm, the Max motor power is 40 * 6.28 = 251 W.
Dynamics
As you correctly said, it is related to the pedalling start, and it affects the e-bike acceleration.
Motor Power Curves
Whenever the e-bike needs to accelerate at low speed, the most power needs to be delivered. (It is also crucial in case of an e-MTB slowly climbing rocks). As the speed builds up, less and less power is needed. Once the e-bike has achieved its high cruising speed on the flat, the power is only needed to counter the rolling resistance and the air drag. Therefore, the power demand drops. Start climbing the hill: the e-bike velocity drops, and more boost is provided by the system.
The e-bike motor system manufacturer can provide different motor curves for different scenarios. An e-MTB has a big boost at low speed range while the boost can be shifted towards higher e-bike velocities for the road cycling scenario.
It is the easiest way to screw up the Motor Power Curve if the user doesn't know what they are doing. For this reason, Specialized never allows the user to access the Power Curves. It is a factory Road or Trail tuning, that's it. I don't recommend even touching the Power Curves in the beginning, if at all!
The Plus modes
I have no idea how Eco+ or Tour+ work.
If I were you, I would install ECO, TOUR, SPRINT and TURBO and only play with Assistance and Max Power.
Hope that helps.