This is a classic case of one phrase having a specific meaning with respect to certification but a different one in a generic sense. The "Critical Engine" which is failed for demonstrating Vmc and Vmcg (with zero crosswind) is effectively the one that will cause the greatest contol problem when failed at a given speed (i.e will need the greatest control deflections). Note that if the failure of each of the engines requires the same control inputs then the "Critical Engine" is usually determined by the sytems operated by that engine, for example the engine that provides the hydraulics for raising the landing gear is a common one.
In the case of a crosswind during the take-off roll, the engine which, when failed, causes the greatest contol problem will not necessarily be the same one as used for determining certification minimum control speeds.