Can't add for more, you explain it very wellIt's the big brother of a VPS.
a VPS (Virtual Private Server) is a smaller slice allocated from a *Dedicated Server*
A dedicated server is essentially a bare metal computer, usually with enterprise level hardware for greater reliability / redundancy that sits in a temperature, humidity and environment controlled building (Datacentre) that runs 24/7.
There are lots of benefits to using a Dedicated Server instead of a VPS, however it depends on your specific use case, as a Dedicated Server could actually be worse, if say your use case was high availability then you'd actually want to go for a Cloud / VPS as it could potentially replicate across multiple Dedicated Servers.
The biggest benefit being is you'll have no noisy neighbours, all the resources/hardware is yours to use how you wish (of course legally).
I hope that helps.