If your company has a resource-consuming website, or just has very precise server configuration requirements, the most relevant option would be a dedicated hosting server.
There is the matter of monitoring the dedicated hosting server and of backing it up. In case of a predicament with your hosting server, like an unresponsive Apache or a network outage.
Some web space hosting providers also provide an extra paid administration service, whereby the company's sysadmins will support you with any predicament that you may encounter.
Together with the option to host your very own domain names, a dedicated hosting server gives you the opportunity to start your very own web hosting corporation and to sell website hosting packages to other people.
The website files on the hosting server can be administered either via a Secure Shell (SSH) connection or through a hosting Control Panel graphical interface like cPanel, DirectAdmin, Hepsia, and so on.
Hosting distributors supply many configurations - from a low-end web server for one single web site to a very powerful architecture that can manage very popular web portals and 1000's of guests at any time.