A startup is a company designed to grow fast. PG, 2012
http://www.paulgraham.com/growth.html
http://www.forbes.com/sites/natalierobehmed/2013/12/16/what-...
a startup is a company designed to scale very quickly
Steve Blank believes a startup is determined by the search of a business model. If you have a business model, then you have a small or new company, not a startup.
https://steveblank.com/2014/03/04/why-companies-are-not-star...
Another distinction worth making, almost its own axis really, is the difference between "a tech business" and "a business that uses tech".
Companies like Cisco, Facebook, Apple, Google, Canonical, and so forth are companies that are tech companies--without their technology, they wouldn't be in business at all. They provide a service or product that is IP in its own right.
Companies like Chipotle, Subway, Uber, Lyft, AirBNB, DoorDash, Dollar Shave Club, and so forth are companies that use tech to achieve economies of scale and growth that wouldn't be as easy otherwise but could still be done. You can imagine a way of making something that to the user is substantially like the Uber today without a complicated backend, even just using call centers and massive dispatch. The key part of their business is part-time contractor drivers, which is a business and not tech innovation.
It's easy to assume that all startups are tech startups, but that's not quite true and it also can limit and slow developing a good business model.
I'm not sure there's such a strong distinction between a tech business and a business that uses tech nowadays.
Facebook was a tech company specifically, and not a company using tech, because the entire product was devoted to rapidly filling social profiles and spinning up the microsites that were user accounts, mining those accounts for information, and then integrating as a platform for advertisers and game developers. None of that tech is really stuff they could've outsourced and still had a business--they couldn't have just white-labeled MySpace for example and gotten away with it.
It means quite different cultures, quite different "correct answers" to similar situations, and has mostly opposite requirements for many business factors and people involved.