Does the desktop browser version of a web site always suffice for the tablet version(assuming no flash)? or is it common for websites to have a special tablet version that is different from both desktop and phone?
Websites can be set up in a way that they adapt to the screen size of the device. I think this is called responsive design, where the design reflows in response to the viewport. This can also be simulated by reducing the width of a browser on a desktop system.
This technique can remove the need to do a separate site version for the purpose. Depending on the need of the site, a full mobile version may be appropriate; in other cases, a responsive design will suffice.
Good articles on the subject:
Examples of responsive designs: http://mediaqueri.es/
Tablets (and phones even worse) have smaller screens than do desktops. Text entry is also more difficult because of the clumsy on screen keyboards (which cover even more of the already cramped screen). So you have to carefully design the site to work well on a very limited amount of space and to require minimal text input (dropdown boxes, selection lists, etc. whereever possible).
Most websites will function adequately on tablets as-is, although you do have to be careful with things like dropdown menus, as there is no concept of "hover" on a tablet.
Many websites actually have a somewhat "better" experience on tablets, because the tablets know how to find the edges of the website and eliminate the unused real-estate (like the white borders you see around this page).
That said, there are many websites that either provide a mobile version of their site (typically auto-detected by the website via the User Agent property of the browser you are using), or give you an app. On phones, due to the very small screen size, this strategy is essential.
It depends heavily on the website, I've seen some that work great on tablets (and phones) with no special tweaks or extra configuration, and some websites that are completely hideous to use. The only way to ever be sure is to try it yourself or wait until a user mentions it.
A simple rule is if there's any level of complexity to the site you'll probably want to revise your approach to the site's UI to cope with the different level of interaction.