I could well be wrong here but I thought the term 'cover' came about in the late 50s to early 60s when pop songs were usually written by professional writers hand given to producers who would suggest them for recording for singers eg, Cilla Black, Tom Jones, Shirley Bassey etc. So it was not unusual ( no pun intended) if the song had crossed the Atlantic say for the same song to be in the charts performed by different artistes. Sandie Shaw and Dion Warwick both covered "Always Something There To Remind Me" by Burt Bacharach and Hal David for example and were rivals with it in the charts.

I understood the term to be related to recorded material, especially where there was a rival element. Simply singing another person's song wasn't regarded as 'covering' it. I don't remember Manfred Mann being referred to as singing Dylan covers.