How is the Catholic religion related to Buddhism?

They aren't really related to each other, and they have only superficial similarities. Roman Catholicism focuses on salvation of the soul through good deeds and faith in Jesus Christ and acknowledging him as the Son of God. Buddhism, which in many ways is more a philosophy than a spiritual religion, focuses on accepting that life is suffering and that letting go of human desires reduces suffering on the way toward nirvana, or enlightenment.