For TV series where the theme song has songwriters, should the lyricists be entered as 'song by' or 'theme by'?

For TV shows like The X-Files, it makes sense to credit Mark Snow as 'theme by', but less clear-cut when individual songwriters are listed in the end credits.

For most Baywatch episodes, there are songs at the beginning and end, with the first – "I'm Always Here" – under the heading 'Baywatch Theme Song, with music by Corey Lerios/John D'Andrea and lyrics by Joe Henry and Jim Jamison. There's also a song at the end, again with songwriters.

For this episode of season five, it seems peculiar to credit Joe Henry and Jim Jamison as 'theme by', and Kevin Savigar and Todd Cerney as 'song writers' when they have ostensibly performed the same task.