ESC doesn't have any connection to efficiency as a function of load. All circuits will be less efficient as you output more amps, ie, at low speeds where the voltage is low but the power stays the same, or under heavy acceleration.

Nowadays ESC simply refers to any circuit you attach to motor and provide with a target speed/torque/power. In common practice yeah ESC/drive controller/motor controller are used interchangeably.

ECU is specifically something else. It's "Engine Control Unit". It refers to the controller for a combustion engine, not a motor.