Side story missions
From PSU Cyril Wiki
Side story missions are spin-offs which continue or add to the plot of story missions. Similar to story missions, side stories are single player only, and will end in failure if incapacitated (even if you are carrying a Scape Doll). These missions differ from normal story missions, however, in that they offer unique sets of rewards either from repeated play-throughs or by clearing certain mission objectives.
Some side story missions have connections to subplots which are required to obtain new NPC partner cards as well as expand on the game's storyline. For further information, please see the following article.