Antisocial vs not being very good at being social

Yes, absolutely.  Also, because my experience with other people throughout life has been negative to a greater or lesser degree, I tend to be very wary and much less inclined to trust too much to others or go out of my way to be friendly with them.  I mostly interact with colleagues at work, and get on with the majority of them.  But I wouldn't want to be friends with them.  And I tend to keep conversations at a phatic level.  I've learned to reciprocate if people ask me about myself or show some interest in what I do.  For instance, people might say 'Did you have a good Christmas', and I'll tell them about my Christmas... but then forget to ask about theirs.  Probably because I'm not really interested in small talk like that.  But, of course, it can seem unfriendly.

I suppose, if I'm brutally honest, I don't really show much interest in other people or what they do.  Perhaps that makes me more 'anti-social'.

Yes, absolutely.  Also, because my experience with other people throughout life has been negative to a greater or lesser degree, I tend to be very wary and much less inclined to trust too much to others or go out of my way to be friendly with them.  I mostly interact with colleagues at work, and get on with the majority of them.  But I wouldn't want to be friends with them.  And I tend to keep conversations at a phatic level.  I've learned to reciprocate if people ask me about myself or show some interest in what I do.  For instance, people might say 'Did you have a good Christmas', and I'll tell them about my Christmas... but then forget to ask about theirs.  Probably because I'm not really interested in small talk like that.  But, of course, it can seem unfriendly.

I suppose, if I'm brutally honest, I don't really show much interest in other people or what they do.  Perhaps that makes me more 'anti-social'.

This sounds exactly like me, it's really difficult to remember to reciprocate with questions like "Did you have a good Christmas?" because it IS very much forced and I can't believe that it doesn't sound forced. While i'm thinking this they've finished with their answer, which I obviously wasn't listening to and it's now my turn to speak - but because I wasn't listening I have no idea what to say next. It's horrible. 

Someone on another forum mentioned being asocial vs being socially inept. As they said

is a person a hermit who chooses not to socialized, or is the person eager to socialize but to inept to do it right, and therefore afraid to socialize?

My reply was .

As for being asocial vs socially inept -surely it is possible to be both? I am both not driven to socialise and also anxious/nervous when I’m put in the position to socialise because I’m quite socially inept.
I can see that it is possible too to be asocial and yet socially skilled.

I guess I'm too asocial to make a big effort to improve on my social ineptness.