If the police weren't called then you weren't charged and you aren't facing crimi al prosecution and as such you won't have a record. I generally advise clients to ignore these civil demand letters. You don't owe them anything. In order for you to owe them something they would have to sue you, (in some jurisdictions prove damages which they most likely couldn't do), and win. Even if they could win, the cost of pursuing this is substantially greater than any amount they can possibly recover so they usually don't. They send out these letters because it doesn't cost much and they are hoping that you don't know better and simply send them the money. Nothing will happen to you if you don't pay it. Take a look at an article in the Wall Street Journal at the link provided below.
This is very fact-specific and the short answer is that you need to sit down with a criminal defense attorney in your area who can properly advise you of what to do and what not to do. In the meantime, don't go back to the store, don't talk to the police, don't pay any money to the store or in response to any letter you receive in the mail, and don't automatically plead guilty to anything. Talk to a criminal defense lawyer ASAP.