Same-sex marriage was recognized by the federal government and incorporated against the states through a series of dramatic court decisions culminating in the Obergfell v. Hodges decision in 2015 which legalized same-sex marriage nationwide. Before the Obergfell Decision, marriage was determined state-by-state. Same-sex marriage was permitted in some states and forbidden in others. The hodgepodge approach to marriage law created a lot of confusion and impacted couples' access to federal benefits.
Prior to the Obergfell Decision, same-sex couples who were married in a state that recognized it could move to any state and have their marriage recognized. States are required to recognize each others' decrees under the reciprocity doctrine. But, that did not mean that states' necessarily enforced court order or other legal documents.
For example, many same-sex couples experienced issues of obtaining divorces in non-recognized states. Additionally, many states declined to enforce out-of-state orders, such as for child support. But, since the Obergfell Decision, same-sex marriage is now legal in all 50 states and the territories.
Another issue that is still encountered by couples today is those who chose to obtain special "domestic partnership" status. Domestic partnerships were state-created civil unions. They enabled couples to access the same benefits as marriage without being married. But these are state-created entities, therefore, other states are not required to recognize them. Therefore, couples who move to non-domestic partnership states are often unable to obtain separation orders, especially since the Obergfell Decision rendered the need for these unions moot.
Are you thinking about filing for divorce? If you are, you should speak with an attorney beforehand. As you can see, there are numerous issues to consider. Sadly, same-sex couples still need to fight their way through bureaucratic morass before they can receive the same benefits. A lawyer can go over the issues that you can expect to confront. You don't need to go through this alone; an attorney can lend a helping hand.