Within narrative concepts there are differences between story telling and story building. Story telling describes the way a story is told in a linear and predetermined fashion to deliver a pre-set and rigid story to the player whereas story building can describe the way a player and a game work together to result in a narrative design through interactions in-game.
There are many ways a story arc can be defined. They mostly all employ the same seemingly slow start and finish but are constructed differently. There is the Double Freytag Triangle, which is comprised of two climaxes, separated by a portion that the story is explained in more detail. Both climaxes have a rise and a fall, but the rise and fall of the first and second climax will differ in content.
Another type of story arc is the Linda Seger "Story Spine". This defines a main plot, but instead of two large climaxes in the story, it comprises of two turning points where the story will take a turn from the expected, leading into a lull and then into another turning point by finally climaxing before the resolution.
Narrative versus Gameplay
“Where gameplay is all about interactivity, narrative is about predestination. There is a pervasive feeling in the game design community that narrative and interactivity are antithetical.” -Mateasand Stern, “Interaction and Narrative”
Narrative and Gameplay are the opposite of antithetical, in-fact it is extremely important that the two are intertwined together. Narrative is the story, whereas Gameplay is how the player interacts with the game to persuade the narrative.
So far I haven't decided on a definitive project idea. I am interested in serious games to help people suffering with, for example, Mental Health and their positive and negative effects. But I am also interested in making fun experiences that make people laugh. For me, it is a toss up between the two. Either a serious game that helps people combat their situations or a fun game that makes people laugh or smile.