This post is actually coming from a direct question from a student in one of my classes. I felt I didn't answer her as best I could, so I thought I would take the time, after gathering my thoughts correctly, to put this topic to rest. First of all, "sociopath" is an actual psychological term used my clinical psychologists, whereas psychopath is not.
Sociopath: the more common label for an individual with antisocial personality disorder (see post on ANTISOCIAL). This is an individual who acts with no conscience. While most people think of serial killers and the sick, twisted individuals portrayed on shows such as Criminal Minds or and of the Law and Order franchises, they are not necessarily homicidal. Most sociopaths are simply extremely selfish--Freud might say they were almost 100% id-driven. They have a tendency to say and do whatever they want without a care for the impact on others. They may borrow or steal money without batting an eye. They may injure someone and not think twice about it. They may impose their will and/or bully someone else into submission for their own convenience. Yes, they may resort to killing and/or torture for the pleasure it brings them, but this type of behavior represents only a small proportion of the sociopaths out there.
Psychopath: using the term psychopathology as a springboard, a psychopath is just a person who exhibits abnormal behavior of any kind. Psychopathology is the study of abnormal behavior. This can include any type of psychological disorder (anxiety disorders, mood disorders, psychotic disorders, dissociative disorders, etc.) or even just someone who "acts weird" in comparison to a subset of the population, such as someone who dresses differently or has an odd way of speaking. Popular media would have you believe that all psychopaths are homicidal as well, but this simply isn't the case. In fact, much like the term "insanity," psychopath is more an invention of culture than an actual scientific, psychological term. The majority of behaviors that fall under psychopathology are actually self-inflicting harmful behaviors. Individual psychopaths very rarely represent harm to others. The greatest chance of being hurt by a psychopath is either a schizophrenic currently experiencing a psychotic episode that incorporates others in some form of delusion or hallucination, or a sociopath with homicidal tendencies, as mentioned above.
That brings me to a "bonus" term for this entry--psychotic.
A psychotic disorder is one in which an individual has a break with the shared view of reality. Organic psychoses such as dementia are caused when parts of the brain begin to deteriorate, leading to malfunctioning of reason and a person's difficulty with sorting out fact from fiction. In the case of schizophrenia (this is NOT multiple personalities!), the individual may suffer from hallucinations--inaccurate or false sensations and perceptions--and/or delusions--false beliefs that are held even in spite of evidence to the contrary. There are other symptoms such as disordered speech patterns, personality disintegration, and disorganized emotional responses that can be found in some forms of schizophrenia. Unlike a sociopath (or antisocial personality disorder), however, most schizophrenics generally do not pose a direct intentional threat to others around them. In fact, they do not live the majority of their lives in one solid state of a psychotic episode, but rather, tend to experience moments to true lucidity between psychotic episodes, especially when under the care of a physician with medical treatment. While schizophrenia is one of the most severe psychological disorders, the actual percentage of the population who can be diagnosed with it is extremely small. In addition, medical and psychological science has come a long way in helping individuals with the disorder control some of the more severe symptoms so that they are able to function in "normal" society on a day-to-day basis.