I think a special interest is where you let this one interest take over your responsibilites and life, even over important stuff like employment. Also it is literally on your mind nearly all the time and talking about it non-stop to a close person really feels good, and you can just talk about it for hours (which is why I get a kick out of talking about my obsessions to an elderly relative with Alzheimer's, she forgets I have been talking about it for the last half hour so I can talk about it all over again, only in different words and she happily listens).
Everybody has interests, it's naive to think ''oh Aspies have special interests so that means nothing interests NTs at all'', because if you think like that then you obviously haven't met an NT, and it's not all about sports and celebrities either. I know NTs who are interested in things like computers, books, films, drawing, science, you name it. But they are more able to push their interests aside (maybe more naturally) and not let their interest take over their life (well, some do plan to follow up a career based on their interest but I will explain about that in a minute), and they don't talk about it non-stop to someone for hours and it's not on their mind continuously.
With the career thing, I know some NTs who enjoy something so much that they want to get a career out of it, like my NT cousin is into computers (knows everything about them, knows how to build them, et cetera), and now he's got a job where he's building computers because that is what he wanted. But with me, I'm obsessed with a certain bus that I get and the drivers that operate it, and it does take over my life; I write loads of stories about them, draw pictures of them, download loads of pictures of the buses in that company, talk non-stop to my mum about the drivers, look forward to getting on the bus more than anything else, getting all upset when one driver I like isn't on it and act like a relative has just died or something, and I want to get a job where I can use this bus to get to it. Now, that is an obsession or special interest, which is a little more extreme than a general interest what NTs have.
_________________
Female
Aged 30
On antidepressants
Diagnosed with AS, ADHD and anxiety disorder
Empathy score: 61 out of a possible 80. (High)