You can create one Application with both a desktop and mobile UI. APEX automatically renders the correct login (and subsequent) pages depending on the screen size.
Both UI's can contain totally different pages and functionality. So in fact you can have two different "applications" within one APEX Application Definition.
You have two options:
- Create one Application with two User Interfaces (with each their own Theme): Desktop (like Theme 26) and jQuery Mobile (Theme 50). Then you have to create every page you want to show up on a particular device in that flavour. So that could mean you have two very similar pages. But of course you can share the background PL/SQL code and the supporting objects.
But in a lot of use cases that isn't really a problem as you are targeting different users with both platforms. Imagine a Conference Planner. You have desktop pages for the people at the office processing registrations etc. And you have a (small) mobile app to plan sessions to attend and evaluate attended sessions. These last functions don't need to be included in the back office system: there only the numbers of attendees per sessions and the ratings are shown as reports.
- Create an application using Responsive Web Design (RWD). Like Theme 25 in APEX (see cloud.oracle.com as an example). Properly created applications using RWD scale and render according to the available screen estate (usually "width"). Creating RWD isn't easy, read https://gocardless.com/blog/unresponsive-design/ for some "inspiration".
But the advantage is: one code base for everything. So when your mobile application should have the same functionality as your desktop application - and also should look "as similar possible", RWD might be your thing.
So pick your favourite ;-)