To answer your initial question, a civil claim essentially means that you face no criminal penalties (i.e. jail/prison time). That being said, if Kohl's files a civil suit against you, yes...you will still have to go to court. However, you will only face monetary consequences if they obtain a judgment against you. It's in Kohl's discretion whether or not to file a civil suit against you. However, please also be advised that to file a criminal misdemeanor charge in Texas generally can take anywhere from a few weeks to a few months depending upon the county in which it is filed.
A civil claim for you is a demand for money for the cost of the security at Kohls in dealing with your theft. Most of these retailers have great camera systems and security that cost money. The store is just attempting to recoup some of their losses. The State has 2 years to file charges against you. The security guy might not be lying to you. He can ask the district attorney's office to bring charges against you. He does not have to do it right away. If the state does charge you, you will definitely have to go to court. You will be charged with a class B misdemeanor which carries a fine of up to 2000.00 and a maximum jail time of 180 days. Then again you might just have gotten lucky and they lost the report. It could be a number of other reasons why you have not been issued a warrant for your arrest. Do not go back to the store to refresh their memory. "Let sleeping dogs lie."
Legal disclaimer: My answers are only intended as general legal advice based on my experience. They are not intended to be a binding legal opinion nor to create an attorney-client relationship.