But let's step back a bit: in jQuery the dollar sign function $ is a shortcut for the main function of the framework which is used to select html elements in the page. This $ method accepts a css-like selector as argument, so if you want to select a specific element by its id you have to use the hash: $("#myElementId") returns a reference to the DOM element boosted by jQuery. We can say it's a shortcut to the usual way of getting a DOM element document.getElementById("myElementId").
It took me a while to understand why I was wrong: the $ method gives a jQuery object that is always an array of Elements, even if the docs say otherwise.
So to the get the real DOM element you have to use $("#myElementId") or the more friendly $("#myElementId").get(0)
So, just to wrap up, $("#elementId") != document.getElementById("elementId"). And comparing to the ASP.NET Ajax Library, it is also different from the $get("elementId") which is exactly the same as doing the getElementById the old way.
It took me a whole afternoon to understand this... I hope this post will save you 4 hours of your time as well.