Sociopath: grows up without a “proper” sense of morality. This is niche-term used by laymans and old psychiatry texts. It is basically a career criminal or a serial offender of society’s rules, an adapted way of living and thinking, but not a true mental disorder.
Psychopath: This is easily the most misunderstood of all. It describes a person born with functional brain abnormalities, the main feature being the inability to process higher emotions like love or remorse and no ability to empathize. They are sometimes very high functioning because they do not get weighed down by emotional considerations; they can become exceedingly rational and devious, and a good amount of them know how to behave favorably in the presence of other people, whether or not the psychopath realizes they are a psychopath–their ability to deceive is almost instinctual.
Antisocial personality disorder: This is purely a DSM label thrown at people that are dysfunctional in their jobs and relationships because they create conflict wherever they go. It is a disorder, but it’s the people around diagnosed ASPDs that tend to suffer most.
The psychiatry bible DSM does not describe the term “sociopath” because it is old and obsolete. Antisocial personality disorder basically absorbed it, even though you can argue it is separate.
More importantly, the DSM does not account for psychopathy at all. Mainstream psychiatry has not caught up with independent researchers, especially in regards to this. There is more than enough evidence on the internet to support that it is a very separate condition.
Basically, the psychopath is a born condition that effects thinking and emotional functioning (and by extent, all decisions involving emotion). They are unable to empathize to any significant degree (which makes them unable to experience love and many other “higher emotions” like remorse, at least in the same way we do). It also effects their usage and response to words with emotional connotations; they sometimes contradict themselves without knowing it because of this (called semantic aphasia).
A psychopath could also have an antisocial personality on top of their primary pathology, and they could also behave like a sociopath because of it.
You can be any combination of the three; sociopath but not antisocial or psychopathic, or both in addition; you could be an antisocial psychopath, or just a psychopath, etc…