Am I the only one confused by this?

In my country, America, we have laws that ban us from having an established religion. Yet our national motto is "In God we trust", before you receive the death sentence, a judge says "and may God have mercy on your soul", not to mention In God we Trust is plastered all over our currency. Mostly because of the religious revival in the 1950's. Basically, God is all over everything here, and we have super religious people. Yet, in the UK, they have an established church, but religion isn't as common and more mellow. That doesn't make any sense to me. Anyone have an opinion?