Cross-Correlation VS Cross-Covariance: Is this really the difference between the two?

[Metronome]

The only difference between the definitions on Wikipedia for cross-correlation and cross-covariance (for deterministic signals) is that cross-correlation shows definite integration, while cross-covariance shows indefinite integration.

Is this really the difference between the two, or is this an artifact of the articles being written by different authors? Does the scaling factor to switch between ordinary correlation and ordinary covariance show up as definite vs indefinite integration in this context for some reason? If not, then what is the difference between cross-correlation and cross-covariance, as the definitions otherwise appear identical?

 

[Bruce]

The cross-covariance article says, "In signal processing, the cross-covariance is often called cross-correlation", so it seems the names are interchangable in that context.

 

[blamocur]

The only difference between the definitions on Wikipedia for cross-correlation and cross-covariance (for deterministic signals) is that cross-correlation shows definite integration, while cross-covariance shows indefinite integration.

The indefinite integral in the cross-variance article seems wrong to me because it is a function of two variables [imath]x[/imath] and [imath]t[/imath], whereas the left hand side shows only one variable.