Neither of the terms are explicitly clinical in nature, and in fact haven't merited a self-contained definition in the DSM. They even, in fact, don't have a solid definition themselves being that they're derived from psychology which is a soft science.
Now if you care to show me endocrine and neurotransmitter dysfunction, or mechanical damage to specific neurostructures modulating common and contrasting features of these 'illnesses' I'll allow you to posture an argument.
If we're being honest though, even the DSM diagnosis is wrong since the 'dysfunction' operates on a spectrum. This is evidenced clearly by the predominance of people with ASPD to hold positions of power (CEOs, government officials, managerial staff, etc...) and the concurrent existence of people with diagnosed ASPD in prison. It may simply be a matter of self-discipline or environment, in either case though it's clear there isn't a starkly contrasted gap between the extremes, but a soft trend with an ideal balance apparently standing in the middle.