Both mean black, but there appears to be a difference in nuance — as practically always when two different words mean (almost) the same thing. I get the impression that ater is more in the direction of "mournful" and niger is more "malicious" or "glowless".
What does Ater mean?
Verb. ater. to send, to deliver.
What is black in classical Latin?
ater, atra, atrum: black (dark) (atrabilious)