Sachi being Yui's mother isn't in the books. She wasn't very well described in the books, so when abec (pronounced ab-eh-she) went to draw her, fans pointed out she looked an awful lot like Sachi, and formulated the theory that while both Kirito and Asuna needed the child to bring them together, Asuna really only required that the child be a girl because of her daddy issues (favouring her brother, which was in the books), and she needed to look like Sachi to keep Kirito grounded in his promise to protect others. Yui and Sachi were never meant to be connected in the books (and Sachi's entire story wasn't in the first two books, it was a side story in the 8th book, so no way was Yui originally meant to be based on Sachi as she came first). However, someone presented abec with the theory (and maybe Reki Kawahara?) and he/they said they liked the theory but it wasn't canon. There may even be a note about it (like "I swear I didn't base her on Sachi") in the art book.

Yui's true parent is the Cardinal system, the AI which runs the original death game. But it's been theorised that she was modeled after Sachi to nail the point to Kirito. Also, Kirito had a younger sister whose relationship with had soured, so he wasn't gonna take on some random little girl unless he had a good reason to. And he kinda does, he treats her as a stray dog Asuna brought home, but warms to her later. Like "aww how cute, you can keep it if you take care of it" kind of thing. But then he fell hard for her and went to some pretty crazy lengths to protect her and now that's his child.

But yeah, put Yui and Sachi side by side. Age aside, I think the biggest difference is, one has a mole and the other doesn't.

They're remaking the first arc of SAO in movies. If they ever get to Yui, even odds they make that connection. I mean, it was right there all along. Kind of like how Game of Thrones fans had Jon Snow's parentage figured out way before the reveal (I mean in the books, but also in the show). Except I think that was always intended.