There are two categories of custody.
Physical custody, or where and with whom the child lives primarily. Visitation is referred to as a period of parental responsibility which implies that it is an obligation or responsibility.
Legal custody is the right to share in major decisions in the child's life, such as health care, education, religion, etc. Usually both parents share legal custody equally. Both physical and legal custody are determined based on what is in the best interest of the child. Absent unusual circumstances, a child needs significant quality time with both parents. Often one or both parents can lose sight of this. Ideally the custody determination will have this as its basis.
Primary physical custody is a major consideration in determining child support.