Do the Illuminati and the Catholic Church have anything in common?

The Illuminati and the Catholic Church both have historical roots in Europe and have been subjects of various conspiracy theories. They share an interest in power and influence, albeit in vastly different contexts: the Illuminati as a secret society aiming to promote Enlightenment ideals, and the Catholic Church as a major religious institution with significant socio-political impact. However, their goals, structures, and beliefs are fundamentally different, with the Illuminati often viewed as a symbol of secularism and skepticism toward organized religion.