Audiences are unaware of most content. The more distance one can create between the original and the cover the more folks get fooled. Time, genre and/or medium will generally do the trick.

Harry Nilsson's cover of Fred Neil's Everybody's Talkin' (Midnight Cowboy) and Whitney Houston's cover of Linda Ronstadt's cover of Dolly Parton's I Will Always Love You (The Bodyguard) trip up a lot of audiences. Real country music nerds will hear the John Doe cover on the juke box in the latter's background.

The Rolling Stones were a 'Top 40 cover band' for their first three albums. The Beatles weren't all that different.

At some point the act becomes a 'tribute' and then an outright 'impersonation.' If one mistakes the present day Elvis for the real deal… there are bigger problems than vocabulary.