Ok folks. let's get technical here (been a while, hasn't it)?
It does have a few weird things about it though which people should bear in mind. Nothing that would stop people from using it, but things people should know.
In Prototype, the $() function returns an HTML element and the Prototype uses the prototype keyword to add extra functionality to the vanilla elements in the page (hence its name).
In jQuery, the $() function actually returns a jQuery object which is bound to the HTML element. This jQuery object then encompasses most of the functionality you will ever need on an element.
For the most part, this is a good thing. By using this strategy, jQuery is non invasive
and will play nice with any other JS framework (it even has a noConflict mode in case you want to use it with Prototype which will assign the $() function to any other combo you want).
However, when you use the $() function in jQuery, then you have to be aware that you are not really calling an HTML element so the standard HTML attributes may not be there.
Here is an example.
Let's say you have a text field
<input name="myTextField" id="myTextField" value="Hello Earth" type="text">
Without jQuery you would have to do this
var myTextField = document.getElementById('myTextField')
In jQuery you can simply use the $() function instead.
var myTextField = $('#myTextField');
However, let's say you need to update its value. You would think this would be the way to do it:
myTextField.value = "Hello Mars";
For some reason though, you find it is not working and this is driving you nuts. Why is this the case?
The reason is that myTextField is actually a jQuery object, not an HTML element. So the way to update a jQuery object's value is by using the val function.
Once you remember that, then you should be plain sailing.
The only thing is that sometimes you may need to call an obscure HTML element attribute like scrollBy. There are plugins to deal with it, but nothing native in jQuery. Currently I am falling back to document.getElementById to get these. This is not necessarily a bad thing because jQuery, as I said before, is non invasive so it leaves the rest of your JS alone (as a good framework should).
I just found out you can use jQuery's get() function in order to access the actual HTML element(s) instead of using document.getElementById. In other words, the following should work:
myTextField.get().value = "Hello Mars";
Note the  is needed because get returns an array of elements.