Unmanaged dedicated servers
Unmanaged dedicated servers are servers that you lease from the hosting company that no other website is using.
The hosting company will still be responsible for the maintenance and upkeep of the server hardware, as well as for the repair of the hardware. The hosting company will not be responsible for any of the other things that go along with the server side applications of your website. Instead you will be given remote access to your server and you will be expected to know how to do these things yourself.
Unmanaged dedicated servers are somewhat less expensive to lease than managed dedicated servers. If you know how to do the server side part of your website management then it may be worth it to spend the extra time in doing it instead of paying the extra for a managed dedicated server. Just keep in mind that time is money. If you are spending too much time managing your server side, you may end up neglecting the very important website upgrades and applications that you need to take care of.