One the most important concept in music rights is that there are two sides to every song, the composition and the recording.
A composition is all the musical components that make up a single piece of music including the melodies, chords, arrangement and lyrics. To put it plainly, the composition is the IP (intellectual property) or the original idea of the song in some tangible form - like a voice memo recording on your smart phone or the lyrics, chords on a notepad.
Also referred to as “work” a composition can have an unlimited number of sound recordings, however every sound recording is its own unique copyright. Dolly Parton wrote and sang "I Will Always Love You" - she owns the publishing or composition plus the sound recording (or her label owns the recording). Whitney Houston's version of "I Will Always Love You" is a different recorded version, of Dolly's composition.
Often times the term is actually a reference to the “composition rights” (also referred to as the “publishing rights” or “the publishing”) which are all the rights associated with the composition. For example, John Lennon and Paul McCartney wrote the Beatles song “Yesterday”, which has been covered by other performers hundreds of times. Each time the Beatles recording or a cover version is performed, John and Paul, as owners of the composition rights, are entitled to performance royalties (the royalties AllTrack collects!). Royalties related to composition rights also include synchronization and mechanicals. Final side note, when someone writes a song, they own the composition rights, even if the song is never recorded.