They differ from regular public schools only in their name, and in that children "may" take a religion class or "may" pray or attend prayer services on a voluntary basis.
And the same goes to Protestant and, as far as I know, Jewish and other "Faith Schools."
This whole situation is secularist-totalitarian and rotten from top to bottom, but it is not analogous to Catholic and other faith-based schools in the US.
Such it sis in Countries without a Bill of Rights, Also more and more often in countries with the Bill of Rights.