You are asking a very interesting question. Is there a difference when praying? If a Catholic, or a Mormon, or a Baptist start a prayer with "our Father who art in Heaven," does it get "routed" differently? Is there some function of what is in someone's mind when they say those words that determines if the prayer is effective or not?
Great question. I am going to side with - no, it makes no difference, they all get "routed" to God.
I would be interested to see other's thoughts.