I think the distinction is that freelancers technically own a company, but what the company does is whatever people ask it to do. Compare a freelancer's company with a company that makes washing machines and you'll notice a substantial difference — I think that's the line here.

That is what I was thinking. Is the distinction having employees?

I would say that's a reasonable way to make that distinction.

What if my employees are freelancers? :)

so you are a freelancer and your employees are freelancers as well, and you're wondering if that makes you owner of a company?

well in that case i wouldn't consider you a company just because you hire freelancers. if you are a person who gets gigs here and there and then passes parts of it to someone else for a cut, i doubt that would be called company. however, if your projects come in at a steady and reasonable rate and you pass parts of them to others to do, also at a steady and reasonable rate, then i think you have a company, good sir!

but of course there are other factors as well: 401K, benefits, etc.

I'd distinguish between consulting and a product company. Product companies license software, sell physical goods, or off-the-shelf goods. Consulting companies sell time to their customer's requirements. They may do fixed-bid work, but the client writes the specs, possibly with help.