Simmed E-Feds use a simulator to determine the outcomes of matches and to write the matches. RP usually has a bearing on the outcome but upsets are common. A lot of prezs use simulators when they don't time to write the matches themselves. Originally, all E-Feds used simulators but eventually the trend shifted to booked.
Booked E-Feds don't use a simulator, they determine the outcome of a match by your RPs, Strategies, Angles, and sometimes your Push. Booked E-Feds usually have written out cards and offer more control over how matches are done. They also make upsets less common than with Simmed E-Feds.
In an Angle E-Fed you still RP but the outcomes of matches are determined by the angles that you start and what kind of push you have going. Angle E-Feds are very rare but they are an interesting alternative.
I have seen a few E-Feds that don't use RPs. All you do is sign up a wrestler and check the page every week or so. These are probably the rarest form of E-Fed but I guess they work for some people.
Before you sign up for an E-Fed you should read all the rules and procedures first. You should find out how they RP, what types of wrestlers they need, if they require strats, and what the skill level of the other wrestlers is. Most E-Feds will have this info on their webpage but if they don't have one the prez will tell you.
Not all E-Feds are created equal. You may rule one but become a jobber in another. It all depends on choosing the right one. The best advice I can give you is to scout the E-Fed out very well before you apply.