No, it certainly is not. It is just another variable name. The $() you're talking about is actually the jQuery core function. The $self is just a variable. You can even rename it to foo if you want, this doesn't change things. The $ (and _) are legal characters in a Javascript identifier.
Why this is done so is often just some code convention or to avoid clashes with reversed keywords. I often use it for $this as follows:
var $this = $(this);
