Definition of a Website (not from wiki)

For example, I have 3 different websites but they are all under the same organization. 1. www.website1.com 2. www.website2.com 3. www.website3.com 4. Parent company: www.parentwebsite.com

However, my client wants to port over all these sub-websites under the parent domain to help save hosting costs: www.parentwebsite.com/website1 www.parentwebsite.com/website2 www.parentwebsite.com/website3

I'm wondering if they do it this way, will it affect their users' attitude towards a certain branding.

When I showed the homepage for www.parentwebsite.com to others, they mentioned that this is a website. However, when I showed the homepage for www.parentwebsite.com/website1 to others, they told me that this is not a website, but it's just a webpage within a website.

Then my question would be, what is the real definition of a website? Is www.parentwebsite.com/website1 considered a website or a webpage, or there is no difference?