I am analyzing the following two urls from John Resig\'s site, but I am not understanding how giving a name to the anonymous function has made a difference.
My understan
Not trying to be combative with Kolink, but he goes a bit too far in saying it is NOT a good example. What #14 has to do with (in the links you shared) are named function expressions (a different animal from function declarations). Regardlesss of where the function reference is passed, if you name your function expression, it will always have a way to call itself, from within itself. This name, that you give your function expression, is a name that only it knows; it does not exist in any external scope.
See here and here on MDN, for a further discussion about function expressions vs. function declarations. The second link, at the bottom, has a heading about named function expressions. It does have a use; see my Gist for an example of one-off recursive function, that adds nothing to the local or global variable scope (useful for one-off DOM traversal, for instance).
Also, Tobias (in his answer here) points out other good uses of named function expressions, namely, in debugging.