Axial Equatorial NMR graph difference
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.