Maybe if by "same voltage" we mean DC voltage the same as AC peak voltage. When we talk about AC voltage we are referring to root-mean-square (RMS) voltage. It's kind of like saying the average, though for math reasons the average of an unbiased sine wave is 0. Anyhooo, 1 VRMS into a load will produce the same power as 1VDC. If AC delivered less power than DC at the same voltage then life would be very confusing.