Paul (or anyone else), in note 3 you say "Starting a company is common, but starting a startup is rare. I've talked about the distinction between the two elsewhere..."
I'd appreciate any links to the places you've mentioned this.
There are millions of small businesses in America, but only a few thousand are startups. To be a startup, a company has to be a product business, not a service business. By which I mean not that it has to make something physical, but that it has to have one thing it sells to many people, rather than doing custom work for individual clients. Custom work doesn't scale. To be a startup you need to be the band that sells a million copies of a song, not the band that makes money by playing at individual weddings and bar mitzvahs.
I'm not sure it's the best way to distinguish, but it is how the term is often used, especially in the context of startup funding, where "startup" is used as a synonym for basically "the kind of thing a VC would want to fund".
I'd appreciate any links to the places you've mentioned this.