The other thing is that it's not uncommon to have people refer to songs as tunes - "I'll sing you the new tune I came across".

Mendelssohn and others of course have written pieces specifically called "Song without words". I think "piece" is as good a word as any to refer to any bit of music, or for that matter set of words.

Or "thing" - "here is a new thing I wrote last week". We wait to hear if it's a tune or a song or a poem or a story. Could be any. (And if it was "A new thing I made" it might be a painting or a cake or a pair of trousers...)

It's all creativity.