It's the language of relativism and political correctness. "Worship" reduces the issue to the mere style and manner of prayer and worship in ceremonies. Religion implies the wider theology, religious ideology and moral teachings which apply to the conduct of life, good vs. evil, etc. Christianity is not just about how people should "worship" privately on Sundays in church services. There are people who play a language game claiming that Christianity is not a "religion" or who like to limit discussions of theological doctrines and moral teachings. And there are secularists and agnostics opposed to all religion who view the "freedom of worship" as quaint and a concession but one which should be kept private and out of the public sphere entirely - i.e., no civic prayer, no prayer in schools, no Christmas Nativity displays in public, no public discussions of religion or religious morality wherever they can file a grievance with the ACLU or the Supreme Court to prohibit that.
Obama doesn't attend Church so people can guess at where he fits in.
Like you said.