I think you distinguished them admirably. It tends to be pretty obvious from context which meaning is intended.

Hell, we use "design language" even if it's clearly not language; i see little reason why this should be different. And of course the rest of the non-verbal chomsky hierarchy has little relation to how most folks use the word (hell, I bet most coders can't even tell you what a regular language is despite using regular expressions).

But, particularly when it comes to stuff like bird song, it shows a lot of features of syntax. I just don't want to throw the baby out with the bathwater arguing over what to call it.