Dedicated server means you have full control of the entire server, including all of the cpu, hard drive, memory etc. In a VPS environment, a dedicated server is 'chopped up' into pieces with each VPS on the server getting a certain amount of processor, memory, and the hard drive which is completely sectioned off from the rest of the server. Each VPS gets it's own operating system, etc. and, other than not having all computing power, you can't really tell it's not the real deal - since you can do everything a dedicated can do.
Also please note that you can get managed or unmanaged VPS and dedicated servers in which you may either have to manage the server yourself and install the OS, or the company may do it for you. If you're new to the whole server thing, I'd suggest getting a managed server, and a VPS because it's cheaper and works like a dedi unless you need the extreme power from one server.
Some companies will chop up a single server into 50 different VDS/VPS servers. Then there are others that chop it into only 10-15 pieces. If you plan on purchasing a VPS, make sure you ask them how many VPS nodes per server on average.
Here's another VPS vs Dedicated article. Honestly, a VPS is the way to go if you're gonna be hosting more than one website - besides most companies offer plans to grow as you grow and if your VPS offers WHM moving to a dedicated server later on is really easy (well it's easy anytime).
A VPS = a low end dedicated server A VPS is not recommended since its speed is pretty slow while a low end dedicated runs faster than a VPS. But it mainly depends on the number of VPS's per server.
More simple logic is that VPS works exactly like a dedicated server but it is virtual and Dedicated server is the one which is physically a server to manage.