All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, you should know that there are two kinds of Fajr:
The False Fajr: It starts before the true Fajr showing its light vertically in the sky from the East in the direction of the West. It is described in the Hadeeth "like the tail of the wolf." It is called false Fajr because its light disappears after its appearance and it is not the true Fajr. This is not the true Fajr by which the time of fasting and the time of the prayer begins; which is the second Fajr.
The True Fajr: It starts when dawn breaks horizontally from the South in the direction of the North. It is called the true Fajr because when its light appears it does not disappear; rather, its light increases gradually. When the true Fajr begins, it is easy to distinguish between the whiteness of dawn and the darkness of the night.
Shaykh Ibn 'Uthaymeen said in Zaad al-Mee’aad, while clarifying the differences between the true Fajr and the false Fajr:
The first Fajr appears approximately half an hour before the second one and then it disappears, and the horizon becomes dark, then the second Fajr appears.
The scholars said: there are three differences between them.
The first difference is that the light of the true Fajr appears to spread whereas the light of the first Fajr [i.e. the false Fajr] is vertical (extending towards the center of the sky).
The second difference is that there is no darkness after the Second Fajr (which is the true Fajr); whereas the light of the first Fajr disappears and the horizon becomes dark after it.
The third difference is that the light of the Second Fajr [the true Fajr] is connected with the horizon; whereas the first Fajr is not. Meaning that the light of the Second Fajr spreads over the earth (atmosphere), whereas between the first Fajr and the atmosphere (horizon) there is darkness.
In the light of the above, the fasting person starts to refrain from eating and drinking when the second Fajr begins, which is the true Fajr and not from the false Fajr. The Hadeeth reads: "There are two kinds of Fajr. One kind, which is the true Fajr, prohibits eating (for the fasting person) and makes the prayer permissible. As for the second kind of Fajr (which is the false Fajr], it does not prevent eating (for the fasting person) nor does it permit the prayer (the Fajr prayer)." [Ibn Khuzaymah and al-Haakim, and they both classified it as Saheeh (authentic)]
Besides, Al-Haakim reported another Hadeeth from Jaabir with the same meaning. However, there is an addition about the Fajr that forbids food: "Its light goes upright in the horizon."; whereas in the first Hadeeth it reads "like the tail of the wolf."
Allah knows best.