How they can fine me outside of court, then summon me to court?

I stole $500 worth of stuff from a store, I paid for a few items. When I was walking out the door a woman stopped me and said "Do you know why I'm stopping you?" My reply was "yes because I'm stupid" She asked me to go with her to the back room and hand over all the stuff I took. I was very cooperative, and polite. They got back everything I took. She had me sign a paper stating I was not allowed back to any of the branch store or I'd be arrested for trespassing. She took my license, height, eye color and a picture of me which she said would not be released its just for the store. She said I would be receiving a fine in the mail no greater than $250. She did however call the police. When he arrived he asked me why I did it, I told him there was no excuse I'm just stupid, and deserve to be punished and arrested. He did not fill out a police report or anything in front of me, and I did not sign anything other than the no trespassing paper from the store. The cop said " You're lucky I did not arrest you, I have 2 DUI's to deal with right now. You will have to go to court, so I hope you learned your lesson, you are free to go." My questions is, do you think they were trying to scare me with the going to court remark? If the store is mailing me a fine, isn't that something that should be taken care of in court, if they are really going to summon me? When I get the fine I will pay it, I just don't understand.