You have Qt libs with SDK for desktop version, they use X11/WINAPI/COCOA like windowing system. For example Qt X11 libs know nothing about cocoa and winapi. But all of them know nothing about qws, that uses by Qt embedded.
Qt embedded use qws server. That's why you have to have Qt embedded builded for your target platform. Because of there are a lot of target platform with different environments, it's impossible to redistribute Qt embedded binary libs, thats why you have to build Qt embedded libs from sources at least for your target device, Additionally you can build Qt embedded for your host device for debugging application using Qvfb (supported only on linux).

But you still able to make application working on Qt embedded and Qt Desktop version as well, all you need to close by #define directive appropriated source code pieces, that use QWS specific code.