The TV Tropes 'trope' that best fits Fiction Branches is Depending on the Writer.
Let's face it. Every character in Fiction Branches (from the 'most certainly exist in every branch' characters of Jon, Karyn, Sarah McMillan, and Jon's possibly deceased grandfather, to the 'quasi-cannon' characters of Zoe, Biff Meadows, Gladys Brewer, Steve 'The Stud' Farber, etcetera) has their characterization differ to various degrees Depending On The Writer. Here are a few examples.
Jon: Is he a scrupulously moral person who will try his best to avoid making any evil or perverted wishes, or one that will get drunk with power? Is he in love with Karyn, or does he just consider her a good friend? Is his last name Madison, Gibson, Merlin, or something else? Does he have a stash of porn, or does the very idea make him blush?
Karyn: Is she in love with Jon, or does she consider him a good friend? Is she straight, lesbian, or bi? Does she really want blonde hair and bigger boobs or is that nothing more than just a careless wish? Does she hate Sarah, or is she just jealous of her? The first episode establishes her as a bit of a tomboy, but how much of a tomboy is she? Is her last name Black or is it something else?
Sarah McMillan: Is she a truly stuck up Alpha Bitch who's mean to Jon, Sarah and other outcasts for no reason, or is she just misunderstood? Is she a Complete Monster, or not such a bad person once you get to know her? Does she really have anything against those not in 'the popular crowd' or does she just not associate herself with them for fear of jeopardizing her social standing? Is she from a wealthy family? Does she have any siblings (prior to the wishing stone possibly giving her some in some branches)?
Jon's grandfather: Is he really dead? What were his real reasons for leaving Jon the stone? Is he still observing the situation from somewhere waiting to step in just in case things get too out of hand, or has something terrible happened to him?
And now, a few of the quasi-canon characters (characters who aren't in the first episode but appear in so many branches with initial defining characteristics pretty much similar or the same that they're considered 'quasi-canon'):
Biff Meadows: Jerk Jock or not so bad once you get to know him? Degrader of women or someone who will stand up and defend his girlfriend's honor? Is he Sarah McMillan's boyfriend, or is he seeing other girls?
Zoe: It's generally agreed that she's Jon's sister and she's a Goth, but how deeply into the Goth lifestyle she is tends to depend on who's writing her and how much that writer is actually interested in or knows much about the Goth lifestyle. If the writer features Zoe in the story but isn't really interested in talking about Goth stuff, her 'Goth' thing is of no more importance than her hair or eye color.
Steve 'The Stud' Farber: Successful ladies' man or just a fool who deludes himself into thinking he's God's gift to women? Harmless idiot or frightening would-be rapist? Loyal friend to Mike 'Moose' Matthews, or a jerk?
Mike 'Moose' Matthews: Generally Steve 'The Stud' Farber's best friend, and usually depicted as not the sharpest knife in the drawer, but his intelligence level varies depending on the writer.
Gladys Brewer: Usually described as overweight, if not 'the fattest girl in the school'. However, whether she's merely fat or obese, or downright grotesque and deformed in appearance, depends on the writer.
And then we get into the manner of Jon and Karyn's other family members. Their parents tend to have different names depending on the branch. Whether Jon's father is alive or dead also depends on the branch as well. Sarah McMillan's family life is also similarly dependent on different writers and different branches.
And of course there's the school. The school that Jon, Karyn, and Sarah go to may or may not even have a name depending on the branch. And its principal and other faculty are also different depending on the branch.
So, all in all, I'd say that if there's one trope that fits Fiction Branches more than any other trope listed on TV Tropes, it's Depending On The Writer.
