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.

That’s true, but my understanding is the main contributor is skin effect, since AC travels only on the surface of the wire, while DC uses the whole area, resulting in lower resistance loss (https://en.wikipedia.org/wiki/Skin_effect)

this iirc is the smallest of 3 problems. the other 2 are skin effect (AC wires only store power on the outside of the wire) and capacitive effects (a write running parallel to the ground is a capacitor and AC current is equivalent to constantly charging and discharging the capacitor)