Few noob question

Few noob question

Hi guys,
 I am new to jquery and got few question.
  1. I am reading this book. The author seems to be using 2 different ways to define a variable. Sometimes he uses var $variableName = (some expression); and sometimes they use and sometimes he uses var variableName = (expression);. So, whats the difference between both?
  2. $(this).someMethod & this.someMethod ===>Are they different?If so,when should I use one or the other?
Thanks for your help,
leet_2k