I believe (not sure) it would be this way:

Music is made by the Composer, which includes vocal melodies.
Lyrics is made by the "Lyrics author", which is only text.

Lyrics are full from your authorship.
The "Composition" is partially yours, once you do vocal melodies.

The term "song writter" is usually for both.

ps: I don't know about copyright law, this is just how i interpret album labels