"Server" is nebulous to us sysadminly types as well. In the large majority of cases what we're talking about is a particular hardware/OS combination, with some forays into dedicated application servers ("The Oracle server"). It comes out of the fact that there is no widely accepted way to lexically discriminate between Server (subtype:Hardware) and Server (subtype:database, subtype:Oracle). You can have servers on servers, so it all gets lumped into 'Server'. Software Engineers build servers out of software, Sysadmins build Servers out of Hardware in order to run Software servers, and sysadmins may end up running those servers as well.
'Server' is highly imprecise when you get down to drawing lines between things like Apache and CentOS.
Where things get really fuzzy is where System Administrator and Application Administrator cross over. In small shops, one person may be doing everything from installing Office 2010 to making sure the PHP/MySQL environment is up to snuff for the one developer in the company. In larger shops that role may be covered by five different people (desktop tech, hardware/OS person, network person, DBA, Web Technology person), three of whom have different concepts of where Server ends and Application begins.
Which is a long way of saying that for StackOverflow, where there is a preponderance of people with formalized Computer Science education, the ServerFault definition of Server can be described in rather precise terms (to a point). On SuperUser, where formal CS training is a very small minority, a more common-sense based definition of Server can be used. Zoredache's verbage is a good one for SuperUser.
Constructing one for StackOverflow will take some doing.
Professional vs. casual:
This is the tone question. Is ServerFault for people with a certain minimum competence in their chosen technology, or is it welcoming to people who are just starting out in all of this? We already have a spate of homework questions getting posted. And there is always that case of the genius Windows administrator dipping their toe into Solaris for the first time and getting stuck. We're still arguing this one.
Scripting vs Programing
I myself have noticed that Powershell questions get better answers here than on StackOverflow. The same is probably true for bash scripts. This is one of those gray areas where complexity can be the differentiator. If you're getting parallel execution working, that's probably a StackOverflow question. If you're wondering how to extract a certain kind of data, that's probably a ServerFault question.
It's all a gray area though. People will go to where the experts lurk, regardless of what the FAQ says.