Bukhari

Hadith Commentary:
Allamah Qastallani rahimahullah has narrated that the sahabah radi Allahu anhum would take a very small pre-dawn meal (suhoor), sometimes just a date or a morsel, and for this reason, a short interval has been mentioned.

It is clearly stated in this hadith that Bilal radi Allahu anhu used to give the call to prayer (adhan) before true dawn (subh sadiq); this was his adhan for suhoor. And Abdullah ibn Umm Maktum radi Allahu anhu would give the adhan for Fajr when people would tell him that dawn had come, because he himself was blind.

Allamah Qastallani rahimahullah says:
“And the meaning in all of this is that Bilal used to give the adhan before Fajr, then he would wait afterwards for supplication and the like, then he would watch for Fajr. When its rising was near, he would descend from there and inform Ibn Umm Maktum, etc.”

That is, Bilal radi Allahu anhu, after giving the adhan before Fajr, would remain at that place for supplication and would wait for Fajr. When the rising of Fajr was near, he would descend from there and inform Ibn Umm Maktum radi Allahu anhu, and then he would give the adhan for Fajr.

The meaning of the short interval between the two adhans is understood in this way. The Qur’anic verse:
﴿حَتَّى يَتَبَيَّنَ لَكُمُ الْخَيْطُ الْأَبْيَضُ﴾ ( al-Baqarah: 187)
also shows that it is permissible to eat suhoor until the white thread (of dawn) becomes distinct. Those who eat suhoor while it is still night are acting contrary to the Sunnah.

According to the Sunnah, suhoor is that after finishing it and before starting the Fajr prayer, there should be an interval equal to the time it takes to recite fifty verses (ayat).

It is not permissible to eat suhoor after the rising of Fajr.

Hadith Commentary:
(1)
Imam Bukhari rahimahullah has selected the Prophetic statement as the title for this chapter. These words have been narrated by Imam Tirmidhi: “Let not Bilal’s radi Allahu anhu call to prayer prevent you from eating the pre-dawn meal (suhoor); rather, it is the true dawn which spreads horizontally across the horizon that is the cause for stopping eating and drinking.” (Jami‘ al-Tirmidhi, Kitab al-Sawm, Hadith: 706)

(2)
In reality, there are two types of dawn:
One is the false dawn (subh kadhib), which rises vertically on the eastern edge of the horizon like the tail of a wolf. At this time, eating the pre-dawn meal (suhoor) is permissible and performing the Fajr prayer is forbidden.
The second is the true dawn (subh sadiq), which spreads horizontally to the right and left of the eastern edge of the horizon. At this time, eating the pre-dawn meal is stopped, and it becomes permissible to perform the Fajr prayer.
Imam Ibn Khuzaymah rahimahullah has explained this subject with a hadith. (Sahih Ibn Khuzaymah: 3/210)

(3)
From this hadith, it is understood that Bilal radi Allahu anhu used to give the call to prayer (adhan) for suhoor. The purpose of this adhan is stated in the hadith in these words: so that those performing the night prayer (tahajjud) may return to their homes, and those who are sleeping may wake up and make arrangements for the pre-dawn meal (suhoor). That is, its name is not the adhan of tahajjud, but rather the adhan of suhoor. (Sahih Ibn Khuzaymah: 3/210)

(4)
Bilal radi Allahu anhu, after giving the adhan, would remain at the same place, recite supplications, and wait for the second Fajr (true dawn). When the true dawn was near, he would descend and inform Ibn Umm Maktum radi Allahu anhu so that he could give the adhan for Fajr. This is the meaning of there being a short interval between the two adhans.
In addition, the pre-dawn meal (suhoor) of the noble Companions radi Allahu anhum was very small in quantity. This short interval between the two adhans indicates the small amount of suhoor of the Companions radi Allahu anhum at that time.
And Allah knows best.