As for your initial point, while some in the field of psychology would content that the two terms/conditions are synonymous (which is implied by the DSM-V, which puts them both under heading of "Antisocial Personality Disorders [ASPD]"). However, while they definitively share may traits, such as a disregard for laws anf the rights of others, in addition to a failure to feel remorse, they have distinct behavioral characteristics, especially when it comes to crime.
According to Scott Bon (Ph.D) and others, "when committing crimes, psychopaths carefully plan out every detail in advance and often have contingency plans in place. Unlike their sociopathic counterparts, psychopathic criminals are cool, calm, and meticulous. Their crimes, whether violent or non-violent, will be highly organized and generally offer few clues for authorities to pursue." The cause of each condition is also different, but you can read more about it
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and
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. (The first hyperlink is to Dr. Bon's article in Psychology Today).