All those sites that are hosted by a dedicated server hosting plan have the server to themselves, or at least the owner. The server is connected to the internet through a series of connections and ports, but they are used by only one person. If you want to increase disk space or change the processor or even add software to the server, you can continue.
You don't need anyone's approval. Basically, hosting on a dedicated server is managed by the website owner. You can easily buy low price dedicated servers via https://www.gigapros.com/portal/dedicated-servers/.
On the other hand, managed dedicated servers are managed by the hosting company that provides the service. This is the best option if you are new to server administration or don't have the time. The hosting company takes care of all the setup and gets you online in no time.
They handle security risks and all kinds of maintenance work. If you need to add software, let them know and they will handle it. It takes a lot of your mind so you can focus more on your business.
If you are using a large site, it is better to let a professional manage the server. Some people won't trust their website to random people, but hosting companies that offer managed dedicated hosting are usually reputable and reliable. It's best to let the pros take care of the servers so they can take care of the technical aspects.