A Startup is an aggressive business, and I think in modern terms it is something which is bridging a gap in the market. Regular traditional businesses are not considered in startups nowadays especially as per the definition of investors because normal business can not achieve huge growth as expected of a startup.

Website is something which is showing the information of an entity it can be a nonprofit organization or a business, so a website is not a business in itself as a startup. I checked your link of BetaPage and I think it is more like a startup