A few minutes ago @BradLawryk asked me on Twitter what the difference between jQuery and jQuery Mobile was. Are they the same thing? Do they work together? Etc. I thought it might make sense to quickly explain how jQuery, jQuery UI, and jQuery Mobile relate to each other. This is my opinion of course so please feel free to chime in.
jQuery UI is a library that works with jQuery. Any jQuery UI page is going to load jQuery first. jQuery UI provides support for widgets and user interaction (think drag and drop for example). You do not have to use jQuery UI to do widgets. In fact, there are about 5 billion jQuery plugins for various widgets. (Give or take a few billion.) Personally I always go to jQuery UI first just because it's easiest and I like the way it does things. You can find out more at jqueryui.com.
That's it. Obviously there's a lot to all of the above, but I just wanted to write something short and sweet that helps clarify the relationship between these 3 tools.