Difference: Ergodic channel capacity and spectral efficiency
Loosely speaking:

Capacity is the supremum of data rate that one can send data with arbitrarily small error probability over a given channel;
ergodic capacity is also the supremum of rate with arbitrarily small error probability, but for fading channels, in assuming the fading process is ergodic, as the term &quot;ergodic&quot; suggests;
spectral efficiency is data rate divided by occupied bandwidth.

Therefore,

Ergodic capacity is not capacity. Capacity is not ergodic capacity. They are channel-specific and we do not necessarily know how to achieve them.
Spectral efficiency is system-specific, i.e. we have already had a system, as said MarcusMuller in his comment. We ignore error probability in using this. Nonetheless, a spectral efficiency is usually implicitly linked with an &quot;acceptable&quot; error probability.

In short, they are very different performance indicators with very different assumptions. In academy, you are free to choose any indicator that supports your research.