The Prophet ﷺ informed us that for the fasting to be accepted:
- Niyyah (intention) to fast is required.
- The time of niyyah is before the break of dawn of the day one is fasting.
عن حفصة زوج النبي صلى الله عليه وسلم أن رسول الله صلى الله عليه وسلم قال: مَنْ لَمْ يُجْمِعِ الصِّيَامَ قَبْلَ الْفَجْرِ فَلاَ صِيَامَ لَهُ
Narrated by Hafsah, Ummul Mu'minin, that the Messenger of Allah (ﷺ) said: "He who does not determine to fast before dawn does not fast."
— Sunan Abi Dawud, Book 14, Hadith 142
Ibn Taymiyyah in his book Al-Fatāwa al-Kubra 5/375 (Arabic only) said that the intention to fast is not tied to being words that are spoken; rather, a thought or deliberation that one will fast suffices as the intention.
As for the three supplications you provided, none of them is attributed to the Prophet ﷺ, and there are no specific words that are known that the Prophet ﷺ used to form his intention of fasting. The reason for using the words provided is, therefore, unknown as they are unattributed in the first place.