To me, embedded system ralates to dedicated applications, including typical parts : manage(control), communicate(connectivity, network), process data (DSP, analyze data, ...)
2 factors are considered when using embedded systems are : compactness and speed (realtime)
A complex system may like above and often is designed with an OS, but so some simple ones just consist of one or 2 parts (such as just control some simple signals)
in this term, Application programming , System programming are not FIELDS just the ways we implemet apps at lower or higher levels (my personal opinion)
And 2 left DSP, Networking, as i can see, are in lots of demand, can't say what is more prevalent
Hope this helps