Often parents will have child support set by the state that they are both living in. So for example if both parents live in NY and there is a NY child support order, then the parents follow the NY Order. That was easy and makes perfect sense.
However, what happens when either (but not both) the paying or the recipient parent moves to another state (for example Florida). Well if nothing else happens then the NY child support order remains in affect and it is just a question of getting the payments to the recipient parent whether that is in NY or in Florida. As a word of advice, it is always a good idea if the recipient parent has relocated to obtaining a certified copy of the order from the original court so that it can be "registered" or "adopted" by the new state if there will be more proceedings.
If the paying parent remains in NY and the recipient parent has moved to Florida and now the Florida parent wants to modify the child support award, NY continues to have "exclusive jurisdiction" over the support order because one of the parents is still a NY resident and is entitled to the application of NY laws. Therefore, child support is calculated under NY laws even if the result might be lower in Florida or if the new state permits emancipation at a younger age.
If neither parent resides any longer in NY then, unless the parents have previously agreed that NY will "continue to have exclusive jurisdiction" over future issues of child support, then the child support order will no longer be exclusively a NY order.
There can be other more complicated situations when there are orders from two different states and one order came from a state that no longer has continuing jurisdiction compounded by what state the parent and child reside. There can be issues about which state has "personal jurisdiction" and which state should hold the hearing and which state's laws should apply.
For these and other many variations that can still occur it is best to speak with an experienced family law attorney as even attorneys often have to refer to the statute for the situations that may not arise on a somewhat regular basis and that are a bit more uniquely presented.