Exactly - they CAN be one and same but not always. My homebase has regular airport picture access badges to, say, drive to the private hangars or air side of FBO and get past main gates, and the SIDA to get behind the commercial side. You can have one or both. As Packrat said there are big "STOP SECURE" signs to go to the areas where SIDA ID needed. I don't have or need a SIDA badge, only airport.

Regarding the OP situation, the whole SIDA badge process and who gets it may have changed. I find it unclear if you are "denied" a SIDA or they just don't deem you need one for your current purposes around the airport. Those are two separate things. I'm not sure the internet could help you.