Rav Shach noticed an argument between Old Tosphot ([תוספות ישנים] )and the regular Tosphot plus Rambam that most people have not noticed. [Old Tosphot is the version of Tosphot before the final editing.]

In a  case of מוציא שם רע (slander) a נערה מאורסה [engaged girl from 12-12.5 ] that has had sex with someone other than her husband gets stoned at the entrance of her father's home. [That is engagement makes her married. "Kidushin" what makes her engaged, and the Hupa is when she comes into her husband's domain;--but she is still married at the engagement. Nowadays, engagement is just an official agreement to get married. That is different from "kidushin".]

But there is also a case of a engaged girl that gets stoned regularly, not at the door of her father's home.

That is when she did not fool him. That is she might let's say have committed adultery when engaged, but after that told her husband and still witnesses come. So there is regular stoning, not at her father's home.

The difference we know from Tosphot [תוספות ישנים] is if she fooled him. [Based on Rav Shila in Ketuboth pages 45 to 46.] That is,--lets says she had sex before the Chupa and then goes through with the Chupa without telling him. Or there was Chupa and she had sex and then sleeps with her husband after that. In these cases to Tosphot she fooled him so she gets stoned at her father's home.

But in Mishna Torah [Laws of forbidden relations chapter 3. Halacha 8 and halacha 10] there are the exact same situations except the difference between regular stoning and stoning at her father's house is if the later case is מוציא שם רע [slander]. That is her husband calls to witnesses and askes them to testify for him.