Joint legal custody means that before a major decision is made regarding the child, the parents consult with one another and try to reach a mutual decision. If a mutual decision is not reached, one parent is usually given the final decision making authority. Sole legal custody means that one parent has the authority to make the decision, but must still inform the other parent of that decision.
In a Joint physical custody arrangement, both parents have significant parenting time with the child, but that time is seldom equal time. One parent is named the residential parent for educational and mailing purposes. A Sole physical custody arrangement is given to a parent who usually has more time with the child than the other parent. The other parent, though, will be given visitation at specific times spelled out in the court papers. The visitation could be substantial, or limited depending upon the best interests of the child.
There is a presumption in Missouri law that that the parents should have joint legal and joint custody of the child.