PG put it best in his essay "Startup = Growth"[1]:
"Let's start with a distinction that should be obvious but is often overlooked: not every newly founded company is a startup. Millions of companies are started every year in the US. Only a tiny fraction are startups. Most are service businesses—restaurants, barbershops, plumbers, and so on. These are not startups, except in a few unusual cases. A barbershop isn't designed to grow fast. Whereas a search engine, for example, is."
A barbershop is a great example of a small business. A barbershop is obviously different in nature from a search engine because it's not designed for rapid growth.
I agree but even this definition feels a bit off to me. If, say, you start a new supermarket chain that is designed to grow rapidly, I wouldn't consider it a startup unless there is some kind of innovation in the business model. That may just be me, but I consider a startup to be a business that is designed for rapid growth and that is doing something new in one way or another.
I'm no expert on the matter, but to me a startup is trying to get big fast, whereas a small business is just trying to make enough money to live comfortably.
A startup nowadays is a business entity that tries to maximize value in the short-term (i.e. flipping), while a small business is a business entity that maximizes value for the long-term.
The problem with long-term stories is that they're usually boring until the business sells or dies.
"Let's start with a distinction that should be obvious but is often overlooked: not every newly founded company is a startup. Millions of companies are started every year in the US. Only a tiny fraction are startups. Most are service businesses—restaurants, barbershops, plumbers, and so on. These are not startups, except in a few unusual cases. A barbershop isn't designed to grow fast. Whereas a search engine, for example, is."
A barbershop is a great example of a small business. A barbershop is obviously different in nature from a search engine because it's not designed for rapid growth.
[1] http://paulgraham.com/growth.html