I think your incorrect about what all prays are for - they are for Allah swt - the Farz, sunnat and nafl including witr - they are all ways in which the prophet pbuh told us to pray to Allah swt.
according to the hanifa madhab its wajib. I'm not sure about the others
so you have
Farz - you have to do
Wajib - you have to do
sunnat - recommanded depedning if its Makouda which are heavily reccomanded and Ghair Makouda which are less
nafl - voluntery