Good question - the answer is no, the two are treated differently and you have different options. Court-Ordered means your ex is disobeying a court order, can be fined and jailed. Contractual means he has breached a contract and you must sue for breach of contract (in the same court the order issued from).
Send a demand letter first - those are free for you to send, but you need to make sure you follow all the requirements. If he fails to pay, file suit and have him served. You might find an attorney to draft the Demand Letter and petition for a flat fee... you should certainly at least have one walk you through the process. Also, St. Mary's in San Antonio has a law school and probably a law library with plenty of resources and forms to look at.