How to call songs where the author has set music on his own / other authors’ poetry

Question

I am not a native English speaker and I compile a list of songs of a certain singer-songwriter.

I try to choose proper words for headings of two major list’s sections:

1. Songs that are written entirely by this author, both lyrics and music.

2. Songs where the author has set music on other authors’ poetry.

I need help to put these draft wordings in order, making them short, clear and correct both stylistically and grammatically. One of my attempts was like this: Songs on his own lyrics / Songs on other authors’ lyrics, but it seems quite awkward to me.

For example, I don’t know which word is right: other authors’, other writers’, other people’ or something else? Likewise, I get confused between lyrics, poems, poetry, words, works and similar words.

Answer 1

On a song-by-song basis, this format is often used¹:

Lyrics by Dean Eikmann, Music by Dorothy Page

or, if one person composed both:

Music & Lyrics by Theresa Jones

So, if your singer/songwriter is Dave Brown, you could use:

Music & Lyrics by Dave Brown

as the first heading, and

Music by Dave Brown

as the other. You could also add a third heading:

Performed by Dave Brown

in the case where he may have performed songs that were written and composed by others.

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¹Examples of this format can be found here and here. Moreover, this page list several songs in both formats, along with songs that were performed by another artist, such as: "The Way We Were" Lyrics by Alan Bergman & Marilyn Bergman, Music by Marvin Hamlisch, performed by Barbra Streisand.

Answer 2

The author of music (the musical notes) is called a composer, whether or not there are words that accompany the music.

As noted in the comment by Jim below, the author of the lyrics (the words/poetry) is called a lyricist.

Someone who does both is often referred to as composer/lyricist or composer and lyricist.

Another form often used is words and music by X.