Mr. Cord is correct if the case and custody determination is being made in Arizona. Texas has different laws and may have different definitions for "joint custody" and "sole custody". Also keep in mind whether you are speaking about physical custody or legal custody. While Arizona doesn't have a "joint physical custody" determination, I have seen it in other states as a way of indicating equal parenting time and sole physical custody would mean that the sole custodian is the parent that has the kids more often. Legal custody, however, likely deals with decision making like it does in Arizona. You should contact a Texas attorney to clarify with them.
The short answer is: A sole custodian makes the major decisions affecting the children - medical, religious, educational, and social. Joint custodians make those decisions jointly with the judge calling any ties.