What is the relation, if any, between jQuery UI and jQuery Mobile?

What is the relation, if any, between jQuery UI and jQuery Mobile?

I am increasingly asked about making our web application adapt easily to the size of the display device.  I found a guy that has done this well using CSS, and he claims he can do this without affecting either the JavaScript the programmeer writes or the server side code (and he gave me the URL fo a page where he is doing precisely that, as well as a online store where he had been contracted to do it (and just successfully finished the contract).  When I asked him about this, and how it is done, he pointed me to his favourite web resources dealing with the topic, and one of the resources he pointed out was jQuery Mobile.  However, when I looked at jQuery Mobile, I saw none of the jQuery UI controls (tab control, accordina, &c.) that I use regularly.

I guess, before the real meat of the question, the first question ought to be, does the CSS in jQuery UI allow a web page that uses a tab control or accordian  to instantly and correctly adapt to the display device size, whether that is a 41 inch HDTV screen connenected, as a monitor, to a desktop computer, or a one inch square pseudo-smart ;-) phonescreen?  (Call me a luddite, but I never saw anything truly smart in these so-called smart phone.)  If not, what would need to be done so that it could?

I will appreciate any insights and pointers to web resources that provide useful information on the question.

Thanks

Ted

The next question is, can a web page use jQuery UI and jQuery Mobile at the same time?