Are capacity and spectral efficiency identical for a dicrete-time digital signal?
The capacity is a property of a channel. A channel can transport no more than a certain amount of information per channel use. When we use a fixed modulation and coding scheme (&quot;discrete-time signal&quot;), this scheme will be able to support a certain amount of information per channel use (which for the channel to support it must be $\leq$ its capacity). It is thus strictly speaking incorrect to speak of the capacity of a certain modulation and coding scheme.
For a given modulation and coding scheme such as a QAM, you can of course compute its achievable data rate in bits per channel use (i.e., per unit bandwidth). You can also interpret this as a spectral efficiency, since it measures how efficient the scheme uses bandwidth (how many Mbit/s do I get for each MHz of bandwidth I invest?). And the results you get may be reminiscent of the capacity since under certain conditions, the schemes can get somewhat close to it.
It is still not the same. Capacity is a property of a channel, spectral efficiency is a property of a transmission scheme (modulation and coding scheme).