In the scenario of B, why would try to hitting on this guy once you aware he is not the one ? and not looking for you true childhood first love ?
in the scenario of A
For the love of god, start from friend again from scratch is just a big no.
From her pov, it doesn't matter if she can remind him that he have this one childhood friend from years ago. If you think of it in more irl view, this mean you could remind him "oh yeah, i did have a friend like that years ago" but the promise never that important to him in the first place and he simple didn't forget it like everything in life. by that point you better just moving on like she did. No point to stick with him, when the promise is not there, this whole relationship is no longer have what key factor of why it exist. So you just flirt with a new stranger and become lover. going for the same guy only like stab yourself in the heart and rebuild an empty shell but the memory, the promise is not there. Heck if that not there he may no longer the same person she in love with, how many year since they last meet ?
Anyways, i expect some twist, from simple like she just look too different than when she was kid so he didn't realize that is her but remember he do have a childhoodfriend and the promise between them. to big twist like he lost his memory. But i lean toward the first one
she did, in the very first chapter