It's quite simple: Netbooks are indeed smaller than notebooks; we usually say that a netbook can have a screen up to 10 inches from corner to corner. Netbooks are cheap and have relatively slow processors, but this is because they are designed for more basic tasks.
You'll also find that netbooks don't have optical drives. They sometimes have Solid State Drives (SSDs) instead of Hard Disk Drives, which are lower capacity but have no moving parts and should, in theory, increase battery life and speed. The last difference is that most netbooks can run either Linux or Windows XP.
Some people look at notebooks and netbooks and think "Why should I buy a device with a 9 inch screen, slow processor, no optical drive for $500, when I can buy a full-featured notebook for the same amount?". The difference is convenience and speed. A netbook is more convenient because it is generally more resistent to the elements, it's lighter, and it usually has a lighweight operating system. The processor itself isn't as powerful, but there's much less processing that needs to be done with Windows XP or Linux in order to be usable.
Netbooks these days come with one of three processors:
1. Intel Atom. Special low-power processor, which you will see in most netbooks.
2. VIA. Another low-power processor by a chip manufacturer who specializes in this stuff. VIA actually has a reference design for netbooks, and a lot of VIA-based netbooks use this exact design. (the Everex Cloudbook and the Astone UMPC are two examples).
3. Intel Celeron M. Not a good idea - it's just a standard cheap notebook processor.
If you're just looking for a portable computer to take along with you on your travels, to check your e-mail, chat on Skype, watch some Youtube videos, write letters, then a netbook is what you want. If you're going to do intensive image editing, multimedia authoring, gaming etc then a notebook is more suited to your needs. A netbook can do those sorts of tasks too, but more slowly. Heck, even a notebook isn't really appropriate for these sort of things.
I mentioned before that netbooks often come with a choice of Windows XP or Linux. I recommend looking seriously at the Linux models. They don't contract viruses, which means your computer doesn't waste power running viruses in the background. They are often cheaper and come with SSDs, which are faster. The Linux distributions that are on these machines are right up-to-date with the latest software, unlike Windows XP which is about seven years old. They are less likely to crash or need reinstallation, their operating system uses less power because it is specifically designed for the low-power platform, and the interface is designed to be very easy to use too.
Whether you buy a Windows or Linux-based netbook, you can run the other operating system on it, but the Linux netbooks use a special modified Linux distribution to give you the easy interface and the low power use.