Re" " They made it sound so much worse than it was. " Stealing from an employer is serious business and the consequences of such actions are often far in excess of the potential profit of the conduct if successful. You are young and your former employer has not over-reacted here, based on the facts summarized in your post. But you will fare better in the future if you do not hold on to notions that this was some sort of trivial error. At somepoint in your future, someone will ask you about it. An answer that makes plain your remorse and the fact of a lesson learned the hard way will serve you far better than one that complains that the employer made "it sound" worse than it was.
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You were actually quite fortunate. If no police were involved and this only involved you and your former employer, you dodged a bullet. Major mistakes can make for very valuable lessons. Make this one of your lessons.
Well this is a first. I disagree with each of my esteemed collegues. I cannot tell whether a complaint will be filed, but it seems that if you did not see a police officer and receive a citation on the spot, you will likely not be charged. I am, however, concerned about these documents you signed which you cannot describe. I don't know, but am concerned, that they may contain a confession. Sounds like it. However, I am neither as judgmental nor as pessimistic about the strengths of the defense as my collegues.
Theft from an employer is known as embezzelment. Ordinary theft of less than $950 is known as a petty theft. Both are "CIMT," or crimes involving moral turpitude. Many jusidictions offer Deferred Entry of Judgment where, on minor first-time offenses such as this, you can take a 6- or 12- hour class and get a dismissal of the charges. You don't want a crime such as this on your record. However, there are post-conviction remedies as well, should the highly unlikely worst case scenario follow.
Petty theft requires a taking with an intent to permanently deprive the owner of the property. Where coupons are freely given out, and without knowing more about the circumstances of the "bust," I can't know how defensible nor how serious your case is. You should consult an attorney to determine the current status. Make no more statements to your employer.