Both the Obama and Trump administration used makeshift jail cells ("cages") to temporarily house migrant children until their cases could be resolved.
Only Trump kidnapped children from their parents. The children detained under Obama came to the U.S. unaccompanied, and the Obama administration tried to find them some kind of permanent accommodations as quickly as possible, but the sheer numbers made that hard to do.
Trump, on the other hand, took kids away from the parents they came with, an action that was cruel, criminal, and completely unnecessary.