berries look the same
but keep in mind when looking
are the leaves opposite of each other on branch
yours are (edit privet have opposite leaves as well)
I may go outside, and look at a privet . (to see if leaves are opposite or alternating )
By the way privet is in the olive family , but berries are said not to be edible
some privet that is not native is taking over in Southern IL.
Now I think In northern IL . our privet that is a ornamental is finally becoming invasive
(some seems to have fruited once in 40 years
I have never saw berries form until a few years ago (and none since)
( but maybe fruited being weather related that year)