Obvious reasons for a custody determination are for the scheduling and enforcement of parenting rights. Whether married or not, but living apart from each other, if there are minor children even parents that get along and manage not to have scheduling difficulties need to have a custody order because circumstances can change over time and the standards for administration of future custody disputes will be influenced by prior agreements and orders.
The factors that the court reviews for an initial custody determination while similar are not exactly the same as considered for a custody modification. If a parent wants to relocate with the child to a distant location it will generally be harder to gain permission then if the court is determining custody for the first time. Of course that assumes that the non-moving parent is actively involved with the child.
The general standard for an initial custody determination is the "best interests of the child". Whereas, in a custody modification or a request for relocation the court will look at the change in circumstances, the reasons, what alternative options are available and the status of the current parenting arrangements.
If there are no prior custody orders or written agreements the court will (in my opinion) not place as a much emphasis on the relocation as they will in determining the roles that each parent has in regard to the child's current development, the need for continuity, the access to other relatives, age and health of the parents and child, incomes of the parents, the current living arrangements and the ability (or lack thereof) of the parents to jointly parent or at a minimum not interfere with the child's relationship with both parents.
Relocation cases are more focused on the need and necessity for relocation and how the child's relationship can be preserved if there is a distant move. The economic reasons for the move are more closely examined, the advantages and disadvantages of the new proposed residence, school district and type of alternative parenting schedule (such as greater periods in the summer, all school recesses and major holidays). Custody modification cases are focused on the unanticipated and substantial change of circumstances of the parents or the child that necessitate a possible change of residence or schedule.
Parents that are no longer living together should consult with a local experienced matrimonial attorney as it is much easier to work things out when things are going well rather than waiting until there is a major disagreement. Even parents that cannot resolve their initial custody/parenting arrangements will be well served going forward by having an order whether resulting from a trial or a written agreement that is negotiated by the parents. Orders and agreements can be enforced and future changes requested will be scrutinized by the court if the parents cannot agree.