The title here may constitute a trick question. There may not BE a difference between the two. As someone who has read extensively on the subject, I can tell you that there is wide disparity in thought and opinion among the experts. According to the information shared in this linked article, data provided by Dr. James Fallon at the University of California, Irvine School of Medicine (who is himself, according to his own evidence, a borderline psychopath), there ARE differences. But I could give you a list of other experts with just as many letters after their name who’d tell you it’s all a bunch of bunk. And then there are some specialists who maintain that there is no such thing as either, but rather that psychopathy/sociopathy occupy a spectrum, much as does autism, and thus no one should label a subject as specifically one or the other.
The debate will doubtless continue. What does Professor Fallon say on the subject, though? If it indeed “takes one to know one,” then he should know what he’s talking about, right? He maintains that, for one thing, psychopaths are more dangerous. But he also says that sociopaths ARE capable of experiencing empathy, or at least of “feeling the emotions of others.” His is the only opinion I have ever heard or read to suggest this. I’m afraid I must remain dubious pending further study and elucidation.

The difference, as I was taught, is that psychopathy is a genetic condition that inhibits empathy with other human beings. The predominant theory, as I was taught, was that it was an evolutionary quirk where, instead of focusing on the good of the whole, you had a subset of humans that were entirely self-focused and thrived off the labors of others. This inclination doesn’t stop psychopaths from being functional members of society – they don’t have to go out and kill people, or hurt others. Its just all in how they emotionally relate to others.
Sociopaths, meanwhile, are entirely defined by their anti-social behavior. They possess all the same empathy as an average human; in fact, sociopaths are often very empathetic towards a single subgroup of people. They’ve developed a mindset that dehumanitizes all others outside this circle, however, and have no compunction about hurting, killing or stealing from the outsiders.