I do believe the actual mechanics for a second serve is different that that for a first serve, of the same kind.
Say we'll talk about the general top/slice.
First serves, toss is more into the court, swing is much flatter, and the point of the serve is to solicit a weak return, or an ace. The toss being more into the court, your swing mechanics change, and you end up farther into the court.
Second serves, hit with more spin, less ball speed, swing about the same speed, the target is much higher, the swing more controlled, the toss more atop the baseline (for staying back) and more into the court (for S/V), so your toss is adjusted to where you want to go. But the ball height over the net is higher, the swing is adjusted to finish upwards more than a first top/sliced serve.
They are different.