Why is the corporate structure important? I like the Wikipedia definition that "A startup is a company, a partnership or temporary organization designed to search for a repeatable and scalable business model." [0] And of course there's "startup culture" which is a group of people focused on iteration, learning, results, etc. Many startups are stand-alone companies, but it's not essential.

[0]https://en.wikipedia.org/wiki/Startup_company