The principal of operation of brushed motors and bldc motors is very different.
Brushed DC motors, you just apply voltage (with 2 wires) and they go. The rotation of the motor physically determines which brushes are in contact with which coils. No control electronics are required. As you said, the motors draw power.
BLDC motors on the other hand have 3 phases, and applying DC voltage to them will do nothing. They need a smart controller to feed power to the 3 phases in a very specific way. This speed controller will have pretty much total control over the power the motor can use. The default mode in vesc is called “current control”, and that’s exacly what it does.