A dedicated server is in simple terms having a full server to yourself.
Advantages here are that you have all the resources of the server at your disposal. This means that you can run one demanding website or many stand websites.
Dedicated hosting is the best way to host a website, however dedicated hosting doesn’t come cheaply. If you have the money to go dedicated you will be getting a very powerful solution for web hosting. 
VPS = Virtual Private Server
This type of hosting is basically a partition of a dedicated server and will work in the same way. It has its own CPU and RAM resources etc. VPS is about half way between reseller and dedicated servers. It has reseller features and dedicated backbone at a price to suit.
Most hosts will allow you to have root access with VPS so you can install what you wish on it.
VPS gives advantages such as:
More Resources for your site(s)
Gives an idea of what a managed server is like
Gives you more freedom and Reseller or shared
This is a step that a webmaster should take if they are stretching reseller limits but cannot afford to buy a dedicated server.
Reseller hosting allows you to create individual sub-accounts from the amount of disk space and bandwidth of your main account. You remain in control by setting the amount of space and bandwidth each sub-account can use. The number of individual hosting accounts (sub-accounts) you can create is unlimited, providing you stay within your space and bandwidth limits.
Shared Hosting is where lots of different website are all sharing and running from the same server. This is the cheapest way to get yourself some webspace. These are also very easy for a webmaster to manage as this is all done from a control panel.
Shared hosting is a good place to start if you are getting into the web. Its cheap and there are a range of facilities that can be availble in different shared hosting packages.
Linux Shared Hosting
This is the best option for shared hosting unless you need facilities such as .asp, .net and MSSQL. If you require these you should use Shared Windows Hosting.
The operating system of your home machine has no affect over the package operating system you choose.
To ensure our services remain on the front line of web hosts we have now introduced VPS hosting.
Virtual Private Servers - http://www.wantingawebsite.com/hosting/linuxvps.php
These give a a lot more flexability than reseller packages.
We have also lowered the prices of our dedicated servers. http://www.wantingawebsite.com/hosting/dedicated.php
See the link for more details.
Our site is currently being redeveloped and deigned for a new look. We have two ideas in mind and we are toying with the two of them. This is the reason if at times the site doesn’t look as it should. Ordering and Customer facilities are online as normal,
Wanting a Website now offer Dedicated Servers. There is little to choose from at this moment in time however this is soon to expand. You can view our pricing and features by clicking here.
There have been a few Linux Shared Package changes:
Web Advanced:
700MB > 800MB Space
20Gb > 30GB Bandwidth
Web Express:
2GB Space
60GB Bandwidth
Premium
4Gb Space
100Gb Bandwidth