How does a conductus compare to the processional hymn?

I would like to know whether, perhaps, the processional part at the opening of a m developed out of the conductus/whether it is a form of conductus... because the role of the conductus is to accompany the priest and, although the processional hymn at the beginning of a m does this, maybe its primary role is to prepare the congregation to meet God. Can anybody clarify? Thanks.