Felix Mendelssohn wrote a collection of pieces called Songs without Words for the piano. This might suggest that the term "song" can be more nuanced than simply whether or not there are vocals.
The original German title is "Lieder ohne Worte" (https://en.wikipedia.org/wiki/Songs_Without_Words), and there is AFAIK no strict requirement for lyrics to count as a "Lied" (or at least "Lied" is not connected to "singen" the way "song" is connected to "sing").