@Billy That is just the textbook definition of the word. If the "song" doesn't have lyrics, the piece of music is classified as something else.
Good morning all...
From my perspective:
A 'song' has lyrics to be sung by singers.
That's self evident to me.
If there's no lyrics it's a
composition or
instrumental.
That differentiation is plain and simple to me.
I like to write songs which is 99% of my efforts.
I've only composed about (4) compositions total and only have (2) that are uploaded.
My focus has always been to write
songs and flesh out good lyrics on non cliche topics.
Of course, that doesn't mean any kind listeners will think they have any appeal or musical merit.

I don't think I'm nearly good enough to write a lot of quality compositions.

So....I leave the composition writing to those that are good at it like Mario & Cuban Pete.
Have a great weekend everyone.