Confusing peltier efficiency COP/Volts and COP/Amps graphs question
COP, coefficient of performance, is a measure of how much heat energy is absorbed on the cold side, per amount of electrical energy needed to drive the Peltier.

There are three things that dump heat into the cold side. The thing you're cooling, heat leak by conductivity from the hot side, and \$I^2R\$ heating in the Peltier.

At very low drive levels, COP is low because the constant heat leak is large compared to the small cooling effect. 

At high drive levels, COP is low because the electrical heating goes up as the square of the current, whereas the cooling only rises as the current.

COP is therefore maximum at some fraction of maximum drive level. The point of maximum varies with the differential temperature across the Peltier, as the heat leak varies with that temperature difference.

Peltiers are so inefficient that they behave mostly as a resistor. While their voltage does vary a little bit as a function of temperature difference, the majority of their voltage drop does look like current times resistance.

There is no fundamental difference between plotting COP, or controlling Peltier operating point, via voltage or current control, they are actually equivalent. If you drive a Peltier from a current source, a voltage will appear across its terminals. If you connect it to a voltage source, then it will draw a current. Once all the temperatures have stabilised, you will have exactly the same voltage and current conditions at the terminals, for any given heat flow and temperature difference.