Correct me if I'm wrong here, but phase and polarity would (sort of) be referring to the same thing for a perfect sinusoidal wave.
Well, this is why it's confusing. It LOOKS the same but it's only the same when you're doing math on paper, or on your oscilloscope, not in the field.
A sine wave shifted 180 degrees looks the same as one which has its relative polarity inverted. But it's not the same signal, in real life.
MATH TIME, ignore if you want.
Example: a sine wave at 100 Hz has a half wave period of 1/200 second, or 0.005 sec, or 5 ms. If you delay a 100 Hz sine wave 5 ms, and add it to the original at the same level, you should get 100% cancellation.
But now your signal is delayed, by 180 degrees of phase, which is 5ms for a 100 Hz wave. Not really the same signal.
Anyhow. When you speak of phase, there are a lot more degrees of it than just 0 and 180, and a LOT MORE MATH.
When you actually want to invert polarity, without delaying a signal at a certain frequency, you (and SD!) should just label the function POLARITY and not phase. Especially if you can remedy it in firmware! Those fancy hardware boxes from B&H can't get a new paint job over the internet!!!