jQuery and jQueryUI are both designed to be added to your website if you want to add a particular feature, jQuery or jQueryUI might be able to help. However, jQuery Mobile is a full framework which is built on jQuery and jQuery UI foundation.
The team announced that the cross-platform jQuery Mobile project under its umbrella is fully deprecated as of October 7, 2021. New technologies for mobile app development have evolved since this project was launched in 2010, so we're encouraging developers to plan for this jQuery Mobile transition.
The framework allows developers to build applications that can be accessed by the widest number of browsers and devices, whether it is Internet Explorer 6 or the newest Android or iPhone. Mobile jQuery also gives developers the ability to render basic content (as built) on basic devices.
jQtouch is optimized for WebKit, jQuery Mobile is looking to support all mobile devices; that is my understanding
some good info here
http://jquerymobile.com/strategy/
and here
http://news.ycombinator.com/item?id=1602169
Additionally to Aaron's answer this is what I've come up with so far:
Apps developed with jQTouch will certainly run fine on iPads and other tablet devices, but we aren’t going to automagically convert to a more tablet-friendly UI that takes advantage of the additional real estate. If you are in need of a JavaScript library that magically updates your UI for everything from small screens, to tablets, to desktops, check out Sencha Touch.
For detailed understanding and to know the differences between mobile frameworks,
you can consider the following link.
http://web.bogdanteodoru.com/resources/mobile-framework-comparasion/
As I discuss on my blog post:
http://zsprawl.com/iOS/2012/04/comparing-jquery-mobile-vs-jqtouch/
I find jQuery Mobile a lot more feature rich and with a lot better cross platform support. JQTouch is very lightweight and great for "form-based" apps that just need navigation. It is missing a lot of the features that users have asked for, and have been turned down, like fixed footers and tabbars.
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