As I understand it, a popular way to discern the two is use the cause of the mental abnormality. If it's neurological in origin, such as odd brain wiring, than you would call it psychopathy. If it's psychological in origin, such as the reaction to a severe childhood trauma, it's sociopathy. Which is to say that psychopaths are born that way and sociopaths become that way. I am not an expert so take it with a grain of salt, I only know this because I've looked it up a lot. There are also some related differences that seemed to be commonly agreed upon, like sociopaths being more inclined to actually caring about very close friends where as psychopaths tend to be completely incapable of it.

Given that definition, it's pretty interesting that Sherlock says he's not a psychopath. If he's a sociopath and the writers/producers are using the above description of the disorders than it suggests that something happened to him that caused him to shut off or mostly ignore the parts of himself that feel and empathize with others. It would be interesting if this is true and could give us material to explore in future seasons of the show.

I know that a common theory among Sherlock scholars (original books, not new series) that support the idea that Holmes is at least a bit of a sociopath is that something happened to his family, likely his mother, that caused him to become obsessed with solving crimes and problems as a way to deal with it. This is further evidenced by Mycroft's similar need to keep things running smoothly and safely. You take two men of unprecedented genius and cause them severe trauma at a young age, perhaps involving an unsolved case, and it's easy to imagine that they both grow up so that their coping mechanisms directly impact what they do with their lives.

This is all hearsay, of course. They could just be using a different definition or it could have been a throw away line/joke.