A psychotic person is anyone experiencing a psychotic break. That is, they have lost contact with reality in some way. That psychotic break can vary hugely in terms of severity. The most obvious example is the person who hears voices. After three or four days off my meds, I might well suffer a psychotic break. But it's important to point out that the majority of people suffering a psychotic break are more of a danger to themselves than to anyone else.
Psychopaths and sociopaths are incapable of feeling empathy. They comprise perhaps 1% of the population. The difference between the two is one of cause. The psychopath's is caused by biology (which we're only just starting to understand) while the sociopath's are caused by their environment (which we understand a little better). The term was coined by Robert Hare and he compiled the checklist commonly used to help diagnose the disorder (it's freely available online if you're interested). When I say that they are incapable of feeling empathy, that means they also cannot feel the emotions which come from empathy: remorse, guilt or conscience (or fear, oddly). They are not necessarily violent. In fact, most psychopaths aren't because they can fulfill their desires lawfully. There are apparently a disproportionate number of psychopaths in politics and the high levels of business because business and politics select for lack of empathy, callousness and so on. The point where they become dangerous is when psychopathy coincides with an urge which can only be satisfied illegally. Usually, but not always, sexual sadism (note that sexual sadism, the paraphilia, is quite different from consensual kink).
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