Delay and sum Beamforming
They're essentially the same, with the steering vector typically representing phase shifts (==delays) using complex numbers from the unity circle, and the weight vector often containing real values to scale the samples. In practice, both can be unified into one and hence, the terms are sometimes used interchangeably. Also note that for many algorithms, the individual amplitude of the samples doesn't matter, and hence, the steering vector's magnitudes can be chosen arbitrarily (as long as non-zero).