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 that is why such 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 told him that dawn had come, because he himself was blind.

Allamah Qastallani rahimahullah says:
wa al-ma‘na fi al-jami‘ anna Bilalan kana yu’adhdhin qabl al-fajr thumma yatarabbasu ba‘da li’l-du‘a’ wa nahwihi thumma yaraqubu al-fajr fa idha qaraba tulu‘uhu nazala fa akhbara Ibn Umm Maktum, etc.
That is, Bilal radi Allahu anhu would give the adhan before Fajr and then remain at that place for supplication and the like, waiting for Fajr. When the appearance of Fajr drew 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 indicates 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.

It is not permissible to eat suhoor after the appearance 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 that dawn which spreads horizontally across the horizon that is the barrier for eating and drinking.” (Jami‘ at-Tirmidhi, Kitab as-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 call the adhan for suhoor. The purpose of this adhan is stated in the hadith in these words: so that those performing tahajjud may return to their homes, and those who are sleeping may wake up and make arrangements for the pre-dawn meal. 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 that 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 Companions radi Allahu anhum would eat a very small amount for suhoor. 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.

535. Commentary:
It is completely correct and permissible for a blind person to give the call to prayer (adhan) or, if he is qualified, to lead the prayer (imamah). As for the adhan, it is evident that someone else will guide him. And nowadays, such clocks have also been invented, through which such people do not face any difficulty in knowing the time.

640. Commentary:

➊ “One would descend and the other would ascend.” This is intended as an exaggeration to indicate scarcity, as such expressions are common in customary speech; otherwise, there would be no benefit in having two calls to prayer (adhan). Imam Nawawi rahimahullah has explicitly stated in most of his books that the beginning of the first adhan occurs in the second half of the night. He says that, according to the scholars, its meaning is that the first mu’adhdhin would remain seated after the adhan, engaged in remembrance and supplication, until the dawn broke and became visible to him. Then he would descend and send the second mu’adhdhin up. This was especially necessary because the second mu’adhdhin, Ibn Umm Maktum radi Allahu anhu, was blind and could not see the dawn, so it was necessary to inform him. However, Hafiz Ibn Hajar rahimahullah, in refutation of this view, says: Along with the clear contradiction to the context of the hadith, there is also a need to identify the specific evidence on the basis of which they have validated this meaning and taken it as intended, to the extent that they deemed it permissible to interpret it in this way. See: [فتح الباري : 125/2]

In any case, it appears that there was not a great interval between the two adhans; it can be described in minutes, not hours—approximately a gap of 20 or 30 minutes. And Allah knows best.

➌ It is established from the narration that the two mu’adhdhins were for the convenience of distinguishing between the two adhans, not so that both would call the adhan together. There would be no benefit in that.