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.

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.

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 CO, the other one feels the effect of -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 interations: 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.

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.