A dedicate server means that 100% of the server resources are yours to use.

With a VPS you have a server that is segmented. Let's say the server has 10 segments. Each of those segments are 100% yours to use, similar to the dedicate server but there are more accounts on the server. You can still do your own software installations and restarts etc.

With shared hosting you will most likely be on an oversold resource and if you approach the resources you pay for you will quickly be cut off.
This is not always the case but it is generally the case in the budget range of hosting.