I thought that psychopathy was the inability to just know that other people have feelings, or that those feelings matter. A high functioning psychopath is someone that has reasoned out that other people's feelings matter (or at least can pretend they do), but it's something they need to think about.
Arguably similar to autism, which I believe is the inability to just know the emotion a person is expressing, as distinct from caring about what emotion the person is feeling.
Psychopathy is clinically typified by diagnostically relevant deficiency of emotional responses to stimuli, profound absence of empathy, and persistent behavioral impulse control issues.
Autism is clinically typified by a wide array of sometimes overlapping symptoms, of which are often included a developmental inability to process emotional signals -- both internal and external -- which can often be interpreted as a lack of empathy, deeply systematic reasoning and sensory processing, and ritualized or "stereotypic"/"repetitive" behaviors.
In the right circumstances an autistic person can be mistaken for a psychopath. I know this from personal experience, in fact (the master of the martial art studio I studied at for nine years denied me a black belt because he believed I was a psychopath. A fact I did not discover until I confronted him on the issue. At the time, my family was still denying me knowledge of my autism diagnosis. I knew something was "wrong" with me, mind you -- but I had no labels for it nor psychiatric assistance tailored to the condition. Things I very much remain bitter to this day for having been denied.)
That being said... it's only rare cases of autism that can be so mistaken, and only by people who lack awareness of autism. One of the easiest distinguishing marks is that the systemic reasoning in autists can result in us having deeply binding ethical beliefs, which is something psychopaths are biologically incapable of having. This can be muddied by the fact that said ethics systems rarely have much overlap with common beliefs. Combined with the deep adroitness with compartmentalization that comes from the lack of self-mirror-empathy and, well.
An example: the first animal I ever killed was a newborn kitten. I won't go into details but it was a premie and it's lungs didn't work right: it was dying a slow and painful death of suffocation and there was no way around that. So I carefully aimed and beat it with a shovel so it wouldn't have to hurt anymore because that was the quickest and surest way of achieving that goal I could think of. I had no affect for a few hours after that because I'd "shut off" my emotions.
My then-girlfriend kept trying to get me to open up and talk to her about it because she was worried, and I didn't understand why. The problem was solved, the animal was no longer in pain. What else was there to worry about? (She, rightly, was worried because I'd never hurt a living thing like that before.)
A psychopath would never have needed to go through that loss of affect, and now that I know my condition I could have recovered it within minutes. So to someone who doesn't know the difference, these could be mistaken for each other. But they are very, very different.
The psychopath merely wouldn't have had an empathic response to the killing at all, so wouldn't have had to block or suppress it.