and yes, poetry can be written without meter, and songs can have irregular meter.

I tend to find completely unstructured poetry has less emotional impact, but taht is not always the case. some of the poems I've read about suffering from mental illnesses, in fact, do really well by incorporating that lack of structure into the content. If there is not a consistent meter, though, I admit I tend to prefer irregular meter changes, instead of a complete lack.

music requires meter by it's very nature, but changing meters within a song is a viable way to create emotional breaks. I consider it a mark of talent, like using discordance in the middle of a song, when used well.

all lyrics are poems. not all poems are lyrics. lyrics are meant to be set to music, it is meant to comprehensible within the rhythm structure of the music it is set to.

not all songs will sound good as spoken word, because lyrics rely on music for support. this will be especially true of lyrics written for a piece of music, as opposed to songs where music was written around the words.

but that's the actual difference. a song is done musically. the lyrics of the song are a poem.

In my years of writing both songs and poems, I have found that many poems don't work as songs, and lyrics that work in a song can seem cliched and insipid when read as a poem. This isn't always the case, of course.

I have heard many musicians say a song is a poem put to music.

Here is a poem by one of Australia's favourite poets "Back to the driving days":
[poetrylibrary.edu.au]
And here is the same poem set to music by Wallis & Matilda about forty years ago:

That is above my pay grade. I think a poem can be written with very little meter, but a song has lyrics, a chorus, and bridges, and the song is then tied to notes, and rhythm. Songs seem more complicated in my mind.