Joan, I've heard a colloquial - I'm not trying to be a neurologist here - description of the perceived similarities, which went thus:
In ASDs, a person has too few filters for sensory & emotional input. This being intolerable or difficult to process, they try to cope by 'shutting down' and blocking off random chunks of input. So it comes across as inept & offensive to NT people.
Sociopaths have extremely rigid filters. Where NT folks are instinctively flexible in our filtering, and decide moment by moment what to block or absorb, people with PDs simply do not receive or process anything outside their fixed filters. (And, as we know, can get very cross if pushed to try!) Because they're able to process what does come in, we take longer to notice there's something missing in their responses.
I know there's some controversy about whether psychopathy is a true personality disorder. Psychopaths process everything but in a different way from the rest of us. Afaik, though, there is an under-developed amygdala which would support the idea that it's a 'pure' expression of sociopathy.