The difference between Obama's Iraq ban 2011 and Trump's current ban is that Obama and his team stopped processing applications for Iraq refugees based on FBI intelligence that they accidentally let a bunch of terrorists in the United States. This also just happened to be during the middle of the Iraq war.
Not saying I support the Obama ban, but at least he had justification for it based on intelligence briefings. Trump's current ban isn't based on FBI or CIA intelligence. It's just a general fly off the handle order.
The bill signed by Obama in 2015 was primarily based on restrictions on visa waivers for those who normally entered without a visa. Basically making them go through the same process as everyone else instead of bypassing the VWP.
The Visa Waiver Program (VWP) is a program of the United States Government which allows citizens of specific countries to travel to the United States for tourism, business, or while in transit for up to 90 days without having to obtain a visa.
That's different than what Trump is doing now. Trump is seemingly banning legal people, people with visas, police are harassing muslims/brown people, and the process has been a disaster.