This is a presumably incomplete list of movies whose soundtracks include different versions of the same song, one sung by characters in the movie, and a cover by a pop artist or artists, which usually (but not always) plays over the end credits. I will not be including songs that were recorded years later for "special edition" soundtracks. (Movies will be listed chronologically.)
1986: An American Tail (soundtrack): "Somewhere Out There", cover by James Ingram and Linda Ronstadt
1991: Beauty and the Beast: "Beauty and the Beast", cover by Celine Dion and Peabo Bryson
1992: Aladdin: "A Whole New World", cover by Peabo Bryson and Regina Belle
1994: The Lion King (soundtrack): "Circle of Life", "I Just Can't Wait to Be King", and "Can You Feel the Love Tonight", covers by Elton John
1995: Pocahontas: "Colors of the Wind", cover by Vanessa Williams
1996: The Hunchback of Notre Dame: "God Help the Outcasts", cover by Bette Midler
1997: Hercules: "Go the Distance", cover by Michael Bolton
1998: Mulan: "Reflection", cover by Christina Aguilera
2013: Frozen: "Let It Go", cover by Demi Lovato
2016: Moana: "How Far I'll Go", cover by Alessia Cara