I think in general the distinction is that a startup can scale more readily than a small business. That's easier to do if you're selling software than, say, haircuts which is why I think the term "startup" is used so much around here.
I think there's also an element of the entrepreneurial mindset on HN. The term "small business" seems to be considered implicitly defeatist here, unless you're (merely) building a "lifestyle business" which excuses your lack of ambition!
I've found that the best definition for "startup" that I've come up with is that a startup is a business that seeks a future liquidity event. A web company that is one guy's lifestyle business selling tv stands isn't a startup any more than a small family owned restaurant. But a restaurant chain like Chipotle is a startup -- at least, until they were bought by McDonalds.
Thus there are startups in and outside the tech world.
If you have a "startup" doing anything else, it's more common to just call it a "small business".