Most water separators are designed to have fuel pulled through them. However, there are some exceptions, the new FASS water separator is a beast and designed to have fuel pushed through it.
You are correct. There are two types of water separators out there. The ones that trap water at the bottom of the separator and they other that has a glass mat design that traps water in the filter media. FASS went to the newer design, that is why they now swap the filter locations on their lift pumps. Only draw back on the glass mat design is once it fills up with water it will not let the fuel pass thru it. It will have to be replaced. I have heard that the glass mat design is better at trapping water but I never had much problem with water in my fuel to begin with. I use the water separator that traps the water at the bottom and honestly have never gotten any water out of it. Never had much of a water problem where I am in MO. Dean