When you are caught shoplifting and a store wants to proceed against you, they can do so civilly and/or criminally.
In your case, the police were never involved and you dealt only with store security. This means that they are not looking to arrest you. That’s good because it means that this incident will never appear on your criminal record.
Instead of involving the police, the store likely had you sign a form which will bar you from that store. You’ll be expected to abide by the stay-away agreement or you can be arrested for trespass if they find you in there ever again.
You have also been told that you will hear from the store's lawyers who will demand that you pay a civil fine. It will be a much higher amount than the value of the property you allegedly stole. This is because your state's civil law allows merchants to charge in excess of what you took to help defray the cost of their security system, their theft insurance, their security personnel and their loss prevention department.
If you pay the fine that should be the last of it and nobody need know anything about this incident because it will not be on your record.
If you don't pay that fine, the store is unlikely to sue you because it would cost them more to do that than what the case is worth. But they can decide at that point to turn your file over to the police and have you prosecuted.
The store can still choose to involve the police for up to 1 year after the incident. After that the statute of limitations runs out on an Jersey disorderly person's offense and the matter would be considered too old to be prosecuted.