Difference between afp and smb

When I check the server preferences, file sharing has turned off by itself. When I try to restart it, it just turns off again

That's clearly not normal. What do the logs have to say?

The users get on via afp. Would smb work better? What's the difference between the two?

AFP was designed by Apple and is the native file sharing protocol in Mac OS X.
SMB was designed by Microsoft and is the native file sharing protocol in Windows.

At one time Macs would use AFP, Windows systems would use SMB. That line is now blurred by the fact that Mac OS X can talk both AFP and SMB, and Windows machines can be persuaded to talk AFP.

There are some under the hood differences and in general your Mac clients should use AFP if possible. Whether SMB is more or less reliable in your case depends on why the server is having these issues in the first place - if it's a resource issue (i.e. not enough memory/cpu/etc.) then enabling SMB is likely to make things worse since the server now has an additional process to keep running.