DD1 is 9 (10 in April) and we finally got a DX of ASD in February of last year. In the past 6 months she has started to become so aware that she is "different" to her peers. She struggles immensely academically. She has never been aware of this before though so it never effected her self esteem or confidence. She was always very much on her own little world. But more recently she has become a lot more self aware. I think it's possibly to do with hormones, she's starting to develop now and is getting spots etc. But she's started saying things like, "I'm stupid, I can't read."
"I don't like school everyone is cleverer than me." 
We do reassure her as much as possible and try to "big up" her strengths as much as we can. But I can see it's only going to start getting worse for her as she gets older and more self aware. She notices that she's only 1 level above dd2 (6) in her reading book, and she knows that kids in her class are reading Harry Potter books. She loves the Enid Blyton Faraway Tree and Wishing Chair books which I've read to her, but some of her classmates are reading them by themselves now and she gets so upset that she can't.
So I'm wondering if trying to explain to her about ASD and what it is and that she has it might help her. That she's not all stupid and just has a condition that makes he brain behave differently sometimes. I don't know how much she'll understand really though, also not sure whether it'll do more harm than good if it just becomes something else that makes her different. 