Different forms of $(document).ready

$ is the jQuery object itself, which when called implements a whole pile of different interfaces. $('string') runs a selector or constructs a node; $(domElement) wraps an element... and $(a_function) is a convenient short hand for $(document).ready(a_function). See the jQuery API docs for (much) more information.

A note in passing: $(function () { ... }) is shorter, but if you ever want to search for all of your on-ready events, you might be wishing that you had .ready to search for :)

There is no difference.

One is a convenient shorthand that calls the other internally.

From the jQuery docs:

A shorthand for $(document).ready(). Allows you to bind a function to be executed when the DOM document has finished loading. This function behaves just like $(document).ready(), in that it should be used to wrap other $() operations on your page that depend on the DOM being ready to be operated on. While this function is, technically, chainable - there really isn't much use for chaining against it.

You can have as many $(document).ready events on your page as you like. See ready(Function) for details about the ready event.