As I remember my music history course, these were originally individual pieces that became associated with certain feasts, periods, or rank of feasts. Obviously, the simpler and lower the liturgical ranking, the simpler the music.
According to the Liber Usualis, there is nothing to prohibit taking the different movements (Kyrie, Gloria, etc) from different mass settings at the same celebration.
There are also a number of each labelled “Cantus ad libitum” or something similar.