When you are looking for hosting there are multiple options. Here is the basic lingo to get you started.
Dedicated Servers: a dedicated server is a server that only has your files on it, such as your website. Unlike shared hosting which may have other companies files or websites. This means that no one elses database or website is going to cause problems for you because your server only has your files.
Managed Hosting: managed by the company you chose, you do not need to deal with managing the server. However the caveat is that you need to understand exactly what the hosting company is willing to manage, it may not be as much as you want. For example they may manage the operating system and patches as needed but may not monitor whether your site is up or down.
Virtual Dedicated Servers: are just as the name implies, they are dedicated to you but virtual. While you do not have an entire physical computer you do have control over the operating system, the flavor and everything else, just as you would with a dedicated server. In a managed hosting environment you may not be able to modify anything at a root level.
Virtual Data Center / Cloud: allows you to scale quickly by ramping up new servers at any time.