There is a nuance which is motive and intent. If I say, "can we bury the hatchet on this one." I am trying to solve a problem. My intent isn't to offend anyone, it isn't to harm anyone. A bully who attacks you verbally only goal is to hurt you.

If you dig a bit deeper it is likely the bully has very low self worth and attacks others to try and have control in their lives which they feel is out of control. Ultimately both the victim and the bully deserve our sympathy because they are both hurting.