Fuuko´s story starts when you aren´t on "best" terms with Nagisa and don´t hug her after the incident with the chorus club (in other words when Tomoya doesn´t become her boyfriend then). Tomoya can meet her serveral times BEFORE her real story though.
He meets her in an empty classroom where she carves "something". After a few "pain-tests" he takes her knife for now. A day later, she grabs him all over (I MEAN it xD) to find it, and after a bit, he returns the knife.
*nothing new till here*
After the chorus-club incident, Tomoya and Nagisa are meeting her in that classroom and Nagisa remembers about her as Ibuki Kouko´s little sister that actually is in a coma after an accident. Since she feels bad for Fuuko, Nagisa takes her home with her. From there on, extreme "Seestar-carving" starts.
They get to know that Fuuko does that to invite the people who get the seastar from her to the wedding of her sister.
Now to the extreme differences to the anime.
None of the other girls are getting a star from Fuuko, and when everyone starts to forget, even Nagisa forgets about Fuuko.
Therefore, Tomoya is on that night before the wedding alone with Fuuko and she "accidently" kisses him.
After the wedding, Fuuko reappears before Tomoya (who doesn´t remember her like in the anime) and asks him (with a seestar in the hands) to go out with her.
