Music publishing can be broken down into two main areas:
1) The composition
2) The sound recording
So automatically two types of revenue can be generated by a song.
So let's take a popular songs such as 'Yesterday' by The Beatles.
When The Beatles version of that song plays both the publishing royalties for the composition AND the recording will be due to the songwriters (Lennon and McCartney) and the performers (The Beatles).
When the song is covered, the original songwriters are still paid their publishing royalties for the composition, however whoever re-recorded the track would be due royalties for the actual sound recording as the royalties are due for a new sound recording which would go to those who are on the new recording (Vocals, instruments etc).
This is just a brief overview of Music publishing, please comment below if you would like to know more about Music publishing in depth and feel free to share this with one who will also find it helpful.