You mean virtual private server, not virtual private network. A VPN is very different from a VPS.
A dedicated server means the whole box is yours to use.
eg
8GB ram
dual quad core CPUs
4TB HDD
A VPS is a dedicated server split into one or more virtual servers.
1GB ram
one core of one of the quad core CPUs
500GB HDD
Each VPS has its own private drive space, other VPSes can't access it etc.
Usually you'd be able to burst to more than one core or a little more ram.