Is Phase and polarity the same thing?

If you reverse (interchange) (+) and (-) wires you shift phase by 180 degrees, at all frequencies. That's why "polarity" (which way the wires are connected) is often described as "in phase" or "out of phase".

When a crossover has a 180 degree phase shift at the crossover frequency (12 dB) connection of the driver out of phase is the right thing to do.

Neither the mic diaphram nor the speaker cone moves in sync with the electrical signal, so it is not as simple as Tbg suggests. Some speaker manufacturers (JBL for example) have the cone pull IN for a positive signal.

Tbg...As I read your comment about some drivers being hooked up out of phase, it seemed as if you had no idea why they would do this. So I explained.

Even if cone excursion matches the electrical signal without delay (doubtful) the resulting sound wave will reach maximum pressure when the cone RATE of movement is maximum...not when the excursion is maximum. That's worth 90 degrees. Similar things with the mic. All in all it's more complicated than you suggest, and it's hardly surprising that opinions vary about phase. Some driver manufacturers (JBL for one) define polarity as cone move IN for a positive electrical input. I learned this when I was connecting a JBL driver in parallel with one of another manufacturer.

Magfan...
6dB..... 90 degrees (not zero)
12 dB...180 degrees
18 dB...270 degrees
24 dB...360 degrees (which is like zero)

Magfan...I rebuilt my MG1.6 crossovers, so I am familiar with them. The low pass (woofer) is 12dB and the high pass is 6 dB. The break frequencies are quite different (I can't remember the exact numbers).

The phase of the passed signal changes over the range of frequencies from below to above the break frequency, with the total change being as I cited. It is not a fixed phase shift. I suspect that there is a frequency between the MG 1.6 high and low break frequencies where the phase difference is closer to 180 degrees than zero, and that's why the tweeter is hooked up "backwards". Physical spacing of the drivers are also a factor. When both drivers are generating sound you want them to be in phase or they will tend to cancel and there will be a sharp notch in the overall frequency response. As a matter of fact, the best way to determine the crossover frequency is to reverse the polarity of one driver and look for that sharp notch.