There is a Midrash (Megillah 14a) that Sarah was really the same as Yiskah (from Gen 11:28), which would make her Avraham's niece, which is pretty close to a sister.
However, Ibn Ezra (Gen 20:12) writes that Avraham was just saying something to appease Avimelekh, and we shouldn't assume it is true. Indeed he addresses your question earlier (Gen 11:28) when he writes that were Sarah the same as Yiskah, your verse should have specified "his granddaughter" as it did with Yiskah's sibling Lot (and mutatis mutandis were Sarah actually Avaraham's half-sister).
This actually has a Halakhic application, as the Talmud (Sanhedrin 58b) in discussing whether or not the Noahide rules of incest apply to a maternal half-sibling cites Gen 20:12 to show that Avraham was being careful to avoid concerns of incest. This would only make sense if Sarah was not the same as Yiskah (as there is no prohibition of incest with a niece, even for Jews). While the Talmud rejects the proof due to the aforementioned Midrash, the Rambam (Melakhim 9:5) rules in accordance with the proof, citing the verse explicitly in his code. Rav Yosef Karo in his commentary there says this is due to its being פשטיה דקרא the simple reading of the verse, while the Midrashic answer is שינויא דחיקא a forced change.
In short: there is a Midrash that they were indeed related somehow, but we are left with your question among others, and the simple reading is that Avraham was just trying to placate Avimelekh and wasn't related to Sarah at all.