Axial Equatorial NMR graph difference I wanted to ask a question about NMR for Axial and Equatorial molecules. 

I was asked to describe how to separate the following two product molecules from this reaction:



and the answer that my colleague mentioned was NMR. 

He stated that for the product on the left, the $\ce{P}$ atoms were in the same environment (axial) so they would show only $1$ peak but on the right hand side product, the $\ce{P}$ atoms were in different environments (equatorial and axial) hence two different peaks would be shown. 

I had a previous introductory course to NMR where coupling constants were discussed, and as the maximum bond coupling "length" was considered to be $3$, this made perfect sense. 

My question is, how are axial and equatorial substituents (if they are the same substituent as in this case) in such different environments? Is it to do with the surrounding substituents deshielding by varying amounts? What is the case?

I failed to find a definitive answer on Google or StackExchange, but only statistical interpretations were given, no actual explanations.
When discussing about same environment and different environment, not only the different position should be noted (axial/equatorial), but also the different electronic effects implied.

In the first case:


In short: the molecule has a plane of symmetry, and the substituents are "mirrored" through the plane.
"Long" explanation: This means that they "see" the same electronic environment: the
equatorial substituents have the same electronic effects on the two
axial substituents. This means that their resonance frequency, is the same.


In the second case:


Short answer: no symmetry exists between the substituents
"Long" answer: every group neighboring the substituents is different. One of the two substituents feels the effects of $\ce{CO}$, the other one feels the effect of -$\ce{O}$-. Except in some unlikely and unlucky cases, this means two different signals.


Note to the reader: shielding, resonance frequencies and NMR behavior arise from (way more) complex interactions: I did not mention, above, any possible effect of non-neighbouring substituents, for instance, neither I talked about the shielding or deshielding effects of near substituents.

Nonetheless, a perception of the "symmetry" of the involved groups might give you a "dirt cheap" and operational insight on what could be the outcome of an NMR experiment, in cases as simple as this.