There are thousands of companies that offer web hosting services on their own server, and it varies greatly according to the services they offer as well, such as own website builder, email services, web design, registrar service etc.
Which web space is selected for your website is usually controlled by the person who builds/develops the website for you. So if you go to a large web design company that has its own server, your website will most likely be left on server/web hosting with them.
When creating your website, I find the web hosting/hosting service that best suits the solution we have come up with. Some CMS systems also function as web hosting, while other solutions mean that CMS and web hosting are separate services. If I e.g. create your website in Wordpress,we must have an external web space, whereas in Webflow everything is included.
Usability
Whether a web space is good or not depends on several things, but security, ease of use and price are factors that are important to emphasize. As a web designer, I prefer web hosting where I can make changes to DNS and name servers myself, which is time-saving when a website is to be published. However, some web hosting does not allow this, so changes have to go via them.
Temporary URL during website development
Another factor I think is important is whether it is possible to create a temporary URL (url) and use it while the website is being developed. If you already have a website and want a new one, a temporary URL allows the website to be up until the new one is finished. That means there's no downtime where you're left without a website.