XLR Pin Vocabulary

Some manufacturers describe XLR pin polarity in a vocabulary of ground, non-inverting, and inverting. Others use a different vocabulary, ground, negative, positive. How does one translate into the other?
The pinouts are the same - it is just a matter of terminology. The correct terminology is inverting and noninverting. A true balanced connection means the cable is connected to a differential input. "positive" and "negative" come from the signs used for noninverting and inverting, respectively, in differential (balanced) amplifiers. Think about the schematic diagram of an op amp - an op amp doesn't have a positive input and a negative input, but rather an op amp has a noninverting input and an inverting input; the pins are labled with a '+' sign (noninverting) and a '-' sign (inverting). And the nomenclature comes due to the input stage, which is a a differential pair. So, in short ground = ground = shield; noninverting = positive; inverting = negative. Just keep in mind that the terms "positive" and "negative" when applied in this manner have nothing whatsoever to do with polarity.
i learn something new here daily. Thanks for the response.
Thanks for clarification
One more note: Industry standard is pin 1 is ground, pin 2 is non-inverting (+) and pin 3 is inverting (-). Some manufacturers do not recognize the standard (we've even seen some using pin 3 as ground) but usually the only significance is that the signal might get inverted if only one of two products connected together is on the standard.
Atmasphere, both my preamp and amp have pin one as the ground. But pin 2 on the preamp is non-inverting and pin 3 inverting, while my amp has the reverse configuration (pin 2 -, pin 3 +). Since the amp is designed to be fully balanced, doesn't the mismatch compromise the sound? Should I have the interconnect cables re-wired, 2 to 3 and 3 to 2?
Kusina -

as "Atmasphere" stated, the only result of using gear with different pin assignments (inverting/non-inverting pins switched) is that the signal will end up being inverted, or reverse polarity. You could have a custom set of interconnects made, with pin 2 going to pin 3, and pin 3 going to pin 2. but then that cable should only be used for those specific pieces of gear. A much easier way to get back to the correct polarity is to swap the speaker cable terminals at one end or the other (not both). That will flip the polarity once again and get you back to where you should be. with either fix, there is no compromise to the sound.
50% of your recordings are out of phase anyway. I would not worry about it too much, unless they are all 2-mic recordings, in which case a phase inversion switch would be handy.