The S Pen is not a stylus. They are not the same at all. A stylus is basically - rubber on a stick. It touches the screen and it works like a finger tip.
The S Pen is a wirelessly charging piece of wacom technology. When it is close enough for "Air view" - it is charging off the battery. It charges when you are using it, not when you are storing it. It has an accelerometer in it, and a potentionometer, showing how long and at what angle you are holding it. It actually can work without touching the screen! It also has a multi-use button. That multi-use button CAN but is not by default used as the same as touching the screen. If the pen is held too far from the device for too long, it has to charge again. There is no way you can actually "click" the button and it sees it as a tap of the screen, but you can touch the TIP of the pen, and when you are just over the top of the screen, it will register it as touching the screen. The Tip of the pen is a button denoting presence of the screen. If in charging proximity, it will draw on the screen. The side button could be awesome, but it is not even coded in most apps.
But in some it is especially useful - like S Note, it is a toggle between "Pen" and "Eraser"
It is very important to understand these differences. I myself carry a ball pen/stylus combo and use it most of the time for a quick task UNLESS I am working on something I need to write down, then I leave the stylus in my pocket and pull out my S Pen which is far more capable.
Congratulations on your Note 2~! Here are some super apps (that I am only affiliated with by using them myself on my own Note 2) that will amp the experience of the note 2, imho
S Pen Toolbox (simple, awesome - allows for great s pen options, inclouding a power option that should be standard with the phone.)
Snap Pad - slides out a customizable "post it" type white board. I made mine transparent so I can still see the screen.
Freenote+ - a college ruled note pad that can render your own handwriting exactly to notes, with a widget you can flip through the pages of. A powerful compliment to the device. I still use S Note, but for creating, importing, overwriting, and exporting PDFs and other "work related tasks." Freenote+ is a light powerful app.
Notification Toggle - put ANY type or number of apps in the notification bar, in one or two rows. (One can be collapsed)
Ink Over Apps - pulls us a very basic paint and tool box on screen. When you hit "paint" - it actually takes a screenshot, but it doesn't save it. IT makes it editable, and if you tap on an icon or link twice, it goes back to a live screen. If you take and mark up screenshots alot, it is awesome.
Hope some other people have some great ones they would care to share!