Simply put - there are some that run off of 3G and WiFi, others just WiFi.
Tablets are 66% computers. Youll never run a full filesystem, true software, etc. But for doing web and email, they seem a pretty good option.
I have a macbook air 13", which is about as thin as it gets. There is a sony Vaio that is also really small and portable, but it is as much if not more than the MBA.
Netbooks have inferior keyboards and screens, as well as lower performance hardware. They have their place too, as theyll likely run as well as a tablet and retain more functionality.
Im not gigging tablets though. The ipad is the gold standard, samsung looks like they offer a pretty awesome one roughly the size of the ipad (not sure of the $$$). Will have to see how things like the kindle fire work out.
Stick with the majors and youll be best off, IMO. Beware of "specs". As an example, my wife's iphone 4 feels as fast for moist stuff as my new 4s (I know, I was running the 4 before I got the 4s), but the 4s battery seems to drain faster. While it may be "faster" in some ways, there are prices to be paid in engineering a device. So, you may not necessarily be wel served by fastest is best unless there is another compelling reason...