Covariance block of MUSIC Algorithm
The IEEE signal processing literature deviates somewhat from the terminology used in statistics and actually from itself so your confusion is justified.
If $\mathbf{x_k}$ is a vector signal the quantity at sample time $\mathbf{k}$,  

$$ \mathbf{R}=
\sum_k \mathbf{x_k \, x_k^H}
$$

is often called either.

The SP transactions historically focused on application areas like like radar, sonar, speech, audio, telephony, .... where the signal propagates in a way where dc isn’t propagated.  The long term time average of amplitude tends to zero.

Music (assumptions) works on 2nd order statistics and is stationary over some interval so implicitly the signal is random.  Under these circumstances the average values of the data will be zero. The algorithm is generally used in array processing.

Typically in IEEE SP papers covariance denotes that the mean vector is subtracted out so the correlation (as shown above) of a zero mean signal vector and the covariance is the same thing.

The interesting thing about algorithms that use 2nd order statistics is that they often work well on deterministic signals. 

Authors in Kalman Filtering papers are more specific.

In Statistics, the Pearson correlation coefficient is not the same as the usage in array processing.

There are more than a few words that have different but similar meaning, like coherence.

Even in SP, the terms mean, average, and expected value are often used in ways that lead to confusion.