Any custody proceeding involving children is going to involve a determination of both legal and physical custody.
"Legal Custody" refers to the legal authority to make major decisions for your children. There are 2 options when it comes to legal custody:
Joint Legal Custody - "[B]oth parents retain full parental rights and responsibilities with respect to their child[ren] and so that both parents must confer on, and participate in, major decisions affecting the welfare of the child[ren]." See SDCL 25-5-7.1.
Sole Legal Custody - one parent shall have the right and responsibility to make the decisions related to health, education and welfare of the children.
"Physical Custody" refers to how parenting time is divided between 2 parties. Parents may agree on the amount of time the children spend with each parent. If parents do not agree, the parenting time schedule set forth herein shall remain in place until a court orders otherwise.
SDCL tit. 25, ch. 4A, app TO CHAPTER 25-4A, Definitions