The policy has been since 1997 that when the parents are detained, the kids are held in a DHS center for up to 20 days. In what was was this not the case for Obama/Bush? I legitimately don't know.
In 2008, President George W. Bush focused on the problem of minors crossing the border without their parents and signed a law unanimously passed by Congress that called for such "unaccompanied minors" to be released into the "least restrictive setting."
By 2014, President Barack Obama was facing an influx of both children traveling alone and families as a result of violence in Central America. At one point, his administration tried housing the families in special detention centers. But after a federal judge in California ruled the arrangement violated a long-standing agreement barring kids from jail-like settings, even with their parents, the government began releasing families in to the U.S. pending notification of their next court date.
Fast forward to Trump, who campaigned on building a border wall, and Attorney General Jeff Sessions, who derided these longtime U.S. immigration practices as "catch and release." Trump and Sessions insisted that people exploit the system, even traveling with children to ensure they aren't jailed and slipping away before their court dates.
SO DID U.S. POLICY CHANGE OR NOT?
Yes. While Trump's new immigration policy doesn't call for families to be separated, as pointed out by Homeland Security Secretary Kirstjen Nielsen, the policy makes separations inevitable.
Following Trump's election, then-Homeland Security Secretary John Kelly now Trump's White House chief of staff floated the idea of separating families as a way to discourage illegal border crossings. But much of the administration's focus went into a travel ban aimed at Muslim-majority nations.
By this April, Sessions announced a plan: The U.S. would have "zero tolerance" for illegal crossings. If a person doesn't arrive at an appropriate port of entry to claim asylum, the crossing is deemed illegal and prosecuted even if the person does not have a criminal history. With the adult detained and facing prosecution, any minors accompanying them are taken away.