Image wise they're relatively the same, However culture wise and what they are.
are two different things.
Oni is Japanese for Ogre, Troll, and even refered to as Demon though the proper name for Demon is yokai.
Oni are commonly massive hideous beings who are often seen wearing animal skin loin cloth and wielding a club to represent that they are invincible. And in Japanese folklore would go and rampage villages even eat humans, Oni were also thought to once be human who had shed their humanity for demon power. However, Oni are losing some of their bad imagery. In some parades men dress up as Oni to chase away bad luck and bring good.
Hannya is a popular no mask used in Japanese theater. A Hannya no Mask represents a jealous female demon. Hannya characters devour men or disguise themselves as beautiful maidens and sleep with men. Hannya also have many other roles. But unfortunately I haven seen too many Japanese Plays so I can't tell you much more than that.