I can not agree with you because what you are saying is obviously not correct. The two series (signals, functions) are not the same, they are defined as two different entities. For example, lets consider that you would like to know if the earthquake activity is correlating or not with the earth tides. You will run a cross-correlation analysis between these two series (supposing you have such data). If they correlate you may conclude that earthquakes might be triggered (in some situations) by earth tides. But again, the tides and earthquakes are different things! Have a nice day.