Wouldn't the key difference be the growth trajectory? I see a startup as a small business that aims to become a big one. Most small businesses are comfortable at their size, but a startup is not. It could achieve that growth by taking on lots of investment, but that's not the only way.
More money pretty much always helps with growth though. The argument is that they're hiring as fast as can be done (to maintain culture/quality/interview-pace) and they have nothing else they can spend money on. It's not impossible.. but it's a bit hard to imagine there is no way at all to increase your workforce productivity. But maybe they're all working 12 hours a day, making huge salaries and eating caviar while getting massages during their breaks
Maybe it does, but it's not the only way. Microsoft, famously, was bootstrapped.