Array gain is not the same thing as "gain," "power gain," "directive gain," or "directivity," but if the noise environment around the array is isotropic and the array input signal is from an isotropic radiator, then array gain is equal to gain defined in the usual way from the array beam pattern.
Array gain differs from "gain," "power gain," "directive gain," or "directivity." However, if the surrounding noise environment for the array is uniform and the incoming signal comes from a uniformly radiating source, then array gain matches the standard gain calculated via the array's beam pattern.