And, to answer your first question, there is no difference between:
var $tab and var tab
They are both JavaScript variables. A variable in JavaScript can begin with a letter, the $ sign, or an underscore character. However, when you're working with JQuery, a common convention is to begin the variable with the $ sign to indicate that the variable contains a JQuery object. This is a clue to you, and anyone else, that you can use JQuery methods on the variable.
In Jake's example, the last two pieces of code create variable called $tab, the variable holds a JQuery object, that he then applies the JQuery find() method to.
Dave