I understand. What this appears to be is the store "giving you a break" by giving you the opportunity to avoid criminal prosecution by paying a fine and fee. Under Virginia law, stores are entitled to recoup via a fine which is generally separate from any criminal charges. I have attached a link to the law here: http://law.justia.com/codes/virginia/2006/toc0800100/8.01-44.4.html
It appears that the store just wants their money (plus any extra fees or expenses incurred by them) and will not report you to police. THIS IS VERY GOOD FOR YOU. The reason it is good is because no criminal charges are/will be filed. If no arrest and criminal charges are filed, you WILL NOT have any criminal history, just like before the shoplifting.
Sometimes stores do this so they can avoid the time and expenses required to contact police, file charges, go to court and testify against you. These resources, the store believes, would be best used for keeping an eye on other shoplifters rather than wasting time with one person (you) going back and forth to court.
So, to answer your question, if you pay the fine, you will STILL not have a criminal history. You would be in the same position as you were in before you walked into the store.
Please let me know if you have any other questions. I would be more than happy to answer them. If not, please click "accept" and leave positive feedback as that is the only way I can receive credit for my response. Thanks!