Anti-social - any behavior that opposes normal behavior as perceived by the society; now this is a pretty vague and broad definition so if you think about, things like getting too drunk and passing out can be perceived as anti-social if the "society" or group of people you associate with are pretty conservative Mormons
- Persistent anti-social behavior is just one of the criteria used to diagnose someone with Anti-social Personality Disorder....former is a sign while latter is a diagnosis...in other words anti-social behavior is to anti-social personality disorder as chest pain is to heart attack....not to mention anti-social behavior is also one of the criteria used to diagnose Conduct Disorder which can only be diagnosed in children and most adults with Anti-Social Personality Disorder were or could have been diagnosed with Conduct Disorder when they were kids
Sociopathic - this term and the term psychopathic are not really clinical terms although they are extensively used in law and popular culture to loosely define a big cluster of individuals who are perceived to be extremely callous and inconsiderate to laws/lives of the society; it is a good term to be used informally and as a sorta "shotgun" method to include all behaviors and personality traits that scientifically belong to many different disorders such as narcissism, lack of guilt, emotionally withdrawn, disregard for others' safety and laws of the society, etc....think of it as an umbrella term that most people have a rudimentary understanding of what it may or may not entail.
Therefore, being anti-social is not necessarily bad depending on whose context it is defined in. My above example of getting too drunk within a Mormon group is most likely anti-social however, get too drunk at a college party and you are perceived as pro-social. Although, there are some universal behaviors that are rightfully considered anti-social no matter the makeup of the society...such as killing small defenseless children .
Hope this clears it up.