In my mind, a startup differs from a small business as follows:
Small Business follows a defined business model, with previous examples of success in the same area with the same model to rely on. As an example, a service provider that founds a business using established practices would be a small business, not a start up.
Start up is defined by its innovation - either in the form of its business model, or the total nature of what it offers. A service provider who comes up with a new service that previously did not exist, or a product developer who comes up with a new product and builds a business around it, would both be examples of a start up.
In essence, a start up is a small business with the added risk factor that it is defined by something new and unknown, whether it be a product, service, marketing angle, or something else. While there is risk in all business ventures, those which are modeled on past successes have history to guide them.
As it has been said for a while in the Lean Startup community, a startup is
a human institution designed to create a new product or service under conditions of extreme uncertainty.What does it mean?
A small business can be an exact clone of an existing business: business model, pricing, product and so on. It is not a startup, because its success depends only on execution. A startup, instead, must search for "a scalable and repeatable business model", so there is first discovery and then execution.
There are likely many answers to this, but here is mine:
A small business is one which a single or small number of owners intend to operate indefinitely for regular profits. Examples include brick-and-mortar retail, personal accounting firms or legal practices, individual vocational services, restaurants, etc. Generally speaking, the owner(s) are the principal workers in the business and make their living from the profits. The value in the business is in its location, its customer base, or in the knowledge that the owner(s) bring.
A startup is a company in which one or more founders intend to invest one or both of time and money, but generally expect a return in the form of a meaningful exit at some point, either through acquisition or (seldomly) IPO. The founders bring meaningful skills to the business but growth is expected to be achieved through hiring, with the founders usually working at a more strategic level on the business as it grows. Profits are generally held and re-invested in the business, with founders often being paid in equity or below-market wages, even if the company is initially successful. Value is held in the intellectual property of the company, which may be in the form of technology, process, or copyrighted work.
To use a real world example, suppose that a web designer starts his own business. He advertises his work at $XX an hour and attracts a number of customers. Over time, he hires a few other designers and they continue to churn out work for a growing customer base. This is a small business, which may someday grow into a very large business, but is not a startup. The value of his business is in the customer base, but the work itself has no lasting value; it is handed off to customers and the next project begun.
Now suppose that same web designer instead designs some sort of common web framework that allows him to develop and host web sites with minimal effort. He hires people to extend that framework, and markets it as a hosted web platform on a contractual basis rather than handing the code off to customers. There is now value in the intellectual property owned by his business, rather than just in the work handed off to customers. This is a startup, and value is built both in the business and in its customer base as it grows.
A startup is an initial phase for any company where it's in its infancy. Failure is a much common occurrence than in later phase companies. In some fields like technology, the failure rate for startups is close to 90%.
When do you move from being a startup to just being a business? that varies. Most say it's when you can rely on your own revenue to operate and do not need further infusions of investment.