As nouns the difference between bully and sociopath
is that bully
is a person who is cruel to others, especially those who are weaker or have less power while sociopath
is a person with an antisocial personality disorder, exhibiting antisocial behavior that usually is the result of social and environmental factors in the person's early life.
As a verb bully
is to intimidate (someone) as a bully.
As an adjective bully
is (us|slang) very good; excellent.
As an interjection bully
is (often|followed by for) well done!.