The "fine" from the store is a "civil demand letter." The store has a right to demand up to $500 from you following a shoplifting incident. If you just ignore their letters, they have to make a decision - sue you in small claims (they almost never do for many reasons) or let it go. Because it's typically not worth their time, they almost never follow through. If there is any restitution, they'll get it back through the criminal case.
The criminal case - the citation you got - that's where you should be concerned. You're looking at theft charges that can carry up to 6 months in county jail (that's not what a first offender would get, but it's the maximum you could get) and/or a thousand dollar fine. The biggest problem is that if you're convicted, you will have a theft case on your record and it will haunt you for years to come.
Your goal should be to avoid a conviction if at all possible. The best way to do that is with the assistance of a good local criminal defense attorney that routinely practices in the court where your case will be heard. There may be factual, legal or other defenses to the charge and a way to get a second chance or reduction of the charge. Start looking for a lawyer now, before your court date.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
Private companies have no legal authority whatsoever to "fine" you or otherwise force you to pay them anything. They could sue you to recover their losses. But, to do so, they'd have to invest a lot of money into mounting a lawsuit. Unless you shoplifted a very expensive item, just the filing fee for starting a lawsuit might be more than what they lost. If that is the case, it is unlikely they will sue.
Mr. Dane is correct. At this time, you should put all your efforts and resources into fighting your criminal charges as those could result in serious consequences if you are convicted. Contact a criminal defense attorney in your area right away.
The response above is not intended as legal advice. This response does not create an attorney-client relationship. Legal questions can only be fully answered through consultation with an attorney to whom you give full and accurate details. Anything you post here is not confidential and is not protected by the attorney-client relationship. It is highly recommended that you seek advice from a criminal defense attorney licensed in your jurisdiction by setting up a confidential meeting.