Well, I’ll give here my understanding of the difference between them, correct me if I’m wrong.
Jquery
The main goal of Jquery is to simplify and somehow standardize cross-browser Javascript, making it easier and handling things like handling HTML elements and making HTTP requests
Jqueryui
It is a set of interface elements (buttons, datepickers, sliders, tabs, these things), made using Jquery, ie, Jqueryui need Jquery to work. (Jqueryui = Jquery User Interface)
Those top two were made for be an addition to your site (either desktop or mobile), adding features like the ones I mentioned above.
Jquery Mobile
Jquery Mobile, unlike the two above, is a complete framework for development. The intention is that it is the starting point of your website. It requires Jquery and uses Jquery and Jquery features to make it easy to build mobile sites.
Another difference is that Jquery and Jquery UI are made to be used as an extra layer in your HTML and CSS. For example, you have a input
to choose date, and turns it into a plugin with Jquery:
$('#meu_input').datepicker();
Jquery Mobile provides ways to choose where these differentiated elements will appear only with the use of HTML:
<ul data-role="listview" data-inset="true" data-filter="true">
<li><a href="#">Acura</a></li>
<li><a href="#">Audi</a></li>
<li><a href="#">BMW</a></li>
<li><a href="#">Cadillac</a></li>
<li><a href="#">Ferrari</a></li>
</ul>
The attribute data-role
tells Jquery mobile to make this list a mobile-friendly component for mobile platforms. data-inset
and data-filter
define attributes of this element, without even using a Javascript line.
I used a little self-knowledge and of that OS question in English to formulate this answer