הַגִּיּוֹרֶת שֶׁנִּתְגַּיְּרָה בִתָּהּ עִמָּהּ, וְזִנְּתָה, הֲרֵי זוֹ בְּחֶנֶק. [...] הָיְתָה הוֹרָתָהּ שֶׁלֹּא בִקְדֻשָּׁה וְלֵדָתָהּ בִּקְדֻשָּׁה, הֲרֵי זוֹ בִסְקִילָה. [...] הָיְתָה הוֹרָתָהּ וְלֵדָתָהּ בִּקְדֻשָּׁה, הֲרֵי הִיא כְבַת יִשְׂרָאֵל לְכָל דָּבָר.
A women who converted with her daughter, and [the daughter] committed adultery [as a Na'arah with Kiddushin], she receives choking. [...] If [the daughter's] conception was not in holiness [i.e. the mother hadn't converted yet] but her birth was in holiness [i.e. the mother had converted already], she receives stoning. [...] If her conception and birth were [both] in holiness, she is like the daughter of a Yisrael for all matters.
The pesukim explicitly prescribe stoning as the penalty for adultery as a Na'arah (Devarim 22:20); however, as the Bartenura points out, this is only in the context of v. 21:
כי עשתה נבלה בישראל
For she has done this disgusting thing in Yisrael
which excludes a convert, who is not part of the general community.
Is this just a Gezeiras HaKasuv that a Na'arah convert doesn't receive stoning for adultery? Or is there a conceptual distinction between a convert and a born Jewess which explains this ruling?