Welcome to JustAnswer.com! My name is DriveFast71(Ron) and I will do my best to answer all of your questions completely and accurately.
Yes, the Service Engine Soon is the same as a Check Engine light. The reason the light went off when the "NEG" cable was removed, as this is the method for "code clearing". The on-board computer now needs to re-boot itself, and re-do a system-wide check (which take a couple of days or 50-75 driving miles, aka "drive cycle").
When the Service Engine Soon (aka Check Engine light) comes on, this is the on-board computer's way of telling you it sees a problem in one of the monitored systems. Unfortunately, there are litterally 100's of parts and sensors monitored in various systems, and to take a "guess" as to which part/sensor in which system is faulty, is virtually impossible. However, if you are not experiencing any drivability issues such as skipping, stalling, shifting problems, etc, then more than likely, the problem is going to lie in the EVAP (emissions) system. Very commonly, this could be a faulty, loose or missing fuel cap or even putting fuel in while the vehicle is running. Check the cap for any cracks in the rubber o-ring on the underside. Check the fuel filler neck for any signs of chips or debris. If these all check out, then the best thing to do at this point is to have the "p-codes" read from the on-board computer. These p-codes are what is used as a "starting point" for the diagnosis and will tell which part/sensor in which system has the fault. Once you get these p-codes you can more accurately and efficiently diagnose the problem and then make the repair. You can have these p-codes read FREE (except in California) at any local "big chain" part store (ie. AutoZone, PepBoys, Advanced, etc). If you still need help after retrieving the codes, you can bring them here, and any of our Techs can walk you through the diagnostic procedure, and then even help you make the repair if you feel confident enough to try.