Yes, there seem to be different pumps (front, rear, headlights if applicable):
https://www.realoem.com/bmw/enUS/sho...diagId=61_2896.
And yes, the windshield pump could be damaged if you tried it when empty: see the
manual, page 63.
Therefore, the auxiliary pumps (rear, headlights) are actually protected by disabling (to save the fluid for the main use) when there's little fluid in the tank (a Check Control warning pops up, do not ignore it
). Thanks for the heads-up about the main one: it's not that I was careless but I did not expect it to be very delicate
!
By the way, the quality of the washer fluid matters: reportedly, the quantity of a "low quality" (anti-freeze, in particular) fluid can fail to be detected correctly and the Check Control warning will persist (so using the original BMW washer fluid can be a valid precaution, but not strictly necessary).