I think the main difference is that social skills are thought of as something that can be learnt. However because of our lack of social instinct as Lorraine Wing put it, or brain difference, as we might say now, we experience difficulties and limits in learning social skills.
I think we probably vary on that area, to the extent we can develop such skills, I tried hard and eventually realised that there was a lack I had been unaware of that was scuppering me, that would be what shows itself to others as the lack of social reciprocity, but to us, we just aren't aware of a need to respond, often, I guess.
So, for us, we often don't do the to and fro responses unless someone else works quite hard to get these from us. Whereas it seems neurotypical people have automatic ability to do that. It's presumably a combination of brain functions, where something doesn't fire the same or is different on our brain mechanisms. I'm aware of slow processing as part of this, sometimes I work out what was meant later on, or feel my feelings later, much later, even years later.
Because of it being a lack, it's hard to work on, though not impossible, in that, once you know there's a lack and that you are missing part of what others communicate or pick up on, it's possible to devise some strategies, such as informing people this may occur, and inviting them to persevere if we seem to be ignoring them in any way.
I guess it's similar to deafness or sight issues in terms of there being possible strategies around it. But it's so little known and usually or often mistaken for rudeness, or something done purposefully.