The word night occurs in many hadith, but what exactly is night time relative to the Prophet's time?
a) Sunset to Sunrise
b) Isha to Fajr
c) Isha to Sunrise
d) Sunset to Fajr
By the sun and its brightness
And the moon when it follows it
And the day when it displays it
And the night when it covers it
During the time of the prophet, as was also the case in the Hebrew world and in pre-Islamic Arabia, the day was not calculated as a twenty-four hour period starting at midnight (as our current system of time does). Rather, each day would marked at sunset, and would consist of two parts, starting with "Night" (ليل) and proceeding to "Day" (نهار).
The Qur'an itself does not define "night" clearly; while there are many references associating "day" with the sun and brightness and associating "night" with darkness and concealment, the exact delineation between the two is not so precise. In fact, according to the classical text
الجامع لأحكام القرآن, Imam Qurtubi claims that God alone knows the exact measure of night, based on the revelation in Surat Al-Muzzammil that "Allah determines the night and the day" (الله يقدر الليل والنهار).
According to Lane's Lexicon, ليل and نهار are opposites, with no intervening period between them. Day, being defined as "the time from the rising of the dawn to sunset", would thus perfectly complement night, which would by extension be defined as the time from sunset to the rising of the dawn (i.e. sunset to Fajr). Similarly, Brill's Encyclopedia of the Qur'an considers the night to include everything from the "evening twilight" (شفق) until "the breaking of morning" (سحر), which immediately precedes the dawn (فلق) itself.
Surat al-Baqarah regulates the nights of fasting until "the white thread of dawn is distinct from the black thread" (يتبين لكم الخيط الأبيض من الخيط الأسود من الفجر), which correlates strongly with the above definitions.
It is important to note that, colloquially, the word ليل (night) can also be overloaded in a similar manner to the English "day", wherein it can be used to refer to an entire 24-hour period (more accurately, an entire period from sunset to sunset) rather than the night-time in particular. The intended meaning is usually clear in context, especially when ليل is used in a pluralized form, but this too needs to be kept in mind.
While there has been significant scholarly interest in the exact definitions of night and day, especially in regards to the transitory periods of twilight and dawn, much of this research was not conducted until significantly after the death of the prophet himself. As such, any references to "night" in the hadith literature were not necessarily (or likely) using the the term in any scientifically precise manner.
According to Muhammad al-Baqir --peace be upon him-- during a debate with a Christian scholar (see here), there is a period of time that neither is considered within day and nor night. But this time is a time from the heavens, Dua is accepted during such times and more, and this occurs between Fajr and Sunrise.
So that means that days are from sunrise to sunset. That is, when the sun is fully formed or at least part of it is viewable in the sky; nights are from Sunset to Fajr. Isha is when night has been settled and the Night of Qadr according to Quran [97:5] is until Fajr.
PS. I couldn't find the original debate's text apparently recorded in (تفسير جامع، ج1، ص412 ـ مفاخر الولايه، كاظميني بروجردي ص 189), but as much as I could remember the same was also true about the interval between Sunset (Qorub) and Maqrib (about half an hour after Sunset). So that I hope someone can find the original text and improve this answer.
There is a huge conflict when it comes to the word "night" in terms of breaking fast in Ramadan. Quran 2:187 states "and seek what God has ordained for you, and eat and drink until the white streak of dawn can be distinguished from the black streak. Then complete the fast until nightfall." Quran states "Fajr" as Sunrise but unlike the precise definition of sun visible in the sky, both Quran and science considers sun on the horizon as Fajr/Sunrise. Fajr prayer ends before the sun starts clearing the dark sky. Similarly "Lail/night" in Quran and science is sun below the horizon i.e. Maghrib/Sunset. The darkness of the sky is not "night" but a part of the night that begins when the sun sets. Hence the parallel ends of the fasting in Ramadan is pretty obvious, sun on the horizon marking the day's beginning and beginning of the night. Colors of the sky changing during night are exactly like the day. The color can vary but the basic concept is the sun above or below the horizon defining day and night. Breaking fast is pretty simple once you understand the beginning of day till the beginning of the night i.e. the white streak of dawn is Fajr/Sunrise and setting of the sun is night time. If night was precisely considered the darkest hour then fast would be ending at Isha time when night has set in completely. Bottom line is the deep logic that the start of the fast is exactly parallel to end of the fast. Also a huge factor in darkness of the sky is weather. On a rainy or snowy day, darkness will cover quickly the sky quickly and will create confusion among people. Thereby creating almost a separate time to break fast for each individual who will follow his own instinct as to when sky feels dark enough to be night. To be uniform and united, fasting will be between sunrise to sunset which is Adhan-e-Fajr to Adhan-e-Maghrib. May Allah guide us all.
To explain "night" in the light of Quran, here are the verses that explain the different stages of night and its darkness making after sunset, beginning of the night. And a sign for them is the night. We remove from it [the light of] day, so they are [left] in darkness.(Surah Ya Sin, 37-40) And the sun runs towards its destination. Such is the design of the Almighty, the All-Knowing. And the moon: We have disposed it in phases, until it returns like the old twig. The sun is not to overtake the moon, nor is the night to outpace the day. Each floats in an orbit.
He created the heavens and the earth in true (proportions): He makes the Night overlap the Day, and the Day overlap the Night: He has subjected the sun and the moon (to His law): Each one follows a course for a time appointed. Is not He the Exalted in Power - He Who forgives again and again? (Surah Az-Zumar, 5)
Among His Sings are the Night and the Day, and the Sun and the Moon. Adore not the sun and the moon, but adore Allah, Who created them, if it is Him ye wish to serve. (Surah Fussilat, 37)
And in the alternation of Night and Day, and the fact that Allah sends down Sustenance from the sky, and revives therewith the earth after its death, and in the change of the winds,- are Signs for those that are wise. (Surah Al-Jathiyya, 5)
By the Night as it conceals (the light); (Surah Al-Layl, 1)
And for part of the night also praise thou Him,- and at the retreat of the stars! (Surah At-Tur, 49)
Stand (to prayer) by night, but not all night,- (Surah Al-Muzzammil, 2)
He merges Night into Day, and He merges Day into Night; and He has full knowledge of the secrets of (all) hearts. (Surah Al-Hadid, 6)
Behold! in the creation of the heavens and the earth, and the alternation of night and day,- there are indeed Signs for men of understanding,- (Surah Al-Imran, 190)
Your Guardian-Lord is Allah, Who created the heavens and the earth in six days, and is firmly established on the throne (of authority): He draweth the night as a veil o'er the day, each seeking the other in rapid succession: He created the sun, the moon, and the stars, (all) governed by laws under His command.s it not His to create and to govern? Blessed be Allah, the Cherisher and Sustainer of the worlds! (Surah Al-Araf, 54)
But those who have earned evil will have a reward of like evil: ignominy will cover their (faces): No defender will they have from (the wrath of) Allah.Their faces will be covered, as it were, with pieces from the depth of the darkness of night: they are companions of the Fire: they will abide therein (for aye)! (Surah Yunus, 27)
And establish regular prayers at the two ends of the day and at the approaches of the night: For those things, that are good remove those that are evil: Be that the word of remembrance to those who remember (their Lord): (Surah Hud, 114)
Indeed, your Lord knows, [O Muhammad], that you stand [in prayer] almost two thirds of the night or half of it or a third of it, and [so do] a group of those with you. And Allah determines [the extent of] the night and the day. He has known that you [Muslims] will not be able to do it and has turned to you in forgiveness, so recite what is easy [for you] of the Qur'an. He has known that there will be among you those who are ill and others traveling throughout the land seeking [something] of the bounty of Allah and others fighting for the cause of Allah . So recite what is easy from it and establish prayer and give zakah and loan Allah a goodly loan. And whatever good you put forward for yourselves - you will find it with Allah . It is better and greater in reward. And seek forgiveness of Allah . Indeed, Allah is Forgiving and Merciful.(Surah Al-Muzzammil, 20)
And it is He who spread out the earth, and set thereon mountains standing firm and (flowing) rivers: and fruit of every kind He made in pairs, two and two: He draweth the night as a veil o'er the Day.Behold, verily in these things there are signs for those who consider! (Surah Ar-Rad, 3)
And He hath made subject to you the sun and the moon, both diligently pursuing their courses; and the night and the day hath he (also) made subject to you. (Surah İbrahim, 33)
He has made subject to you the Night and the Day; the sun and the moon; and the stars are in subjection by His Command: verily in this are Signs for men who are wise. (Surah An-Nahl, 12)
We have made the Night and the Day as two (of Our) Signs: the Sign of the Night have We obscured, while the Sign of the Day We have made to enlighten you; that ye may seek bounty from your Lord, and that ye may know the number and count of the years: all things have We explained in detail. (Surah Al-Isra, 12)
“Perform As Salaat (Iqamaat as Salaat) from mid day till the darkness of the night (i.e. the Zuhr, ‘Asr, Maghrib, and ‘Ishaa’ prayers), and recite the Qur’aan in the early dawn (i.e. the — Fajr morning prayer). Verily, the recitation of the Qur’aan in the early dawn (i.e. the morning — Fajr prayer) is ever witnessed (attended by the angels in charge of mankind of the day and the night)” (Surah Al-Isra, 78)
And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory! (Surah Al-Isra, 79)
Therefore be patient with what they say, and celebrate (constantly) the praises of thy Lord, before the rising of the sun, and before its setting; yea, celebrate them for part of the hours of the night, and at the sides of the day: that thou mayest have (spiritual) joy. (Surah Ta Ha, 130)
It is He Who created the Night and the Day, and the sun and the moon: all (the celestial bodies) swim along, each in its rounded course. (Surah Al-Anbiya, 33)
It is He Who gives life and death, and to Him (is due) the alternation of Night and Day: will ye not then understand? (Surah Al-Muminun, 80)
It is Allah Who alternates the Night and the Day: verily in these things is an instructive example for those who have vision! (Surah An-Nur, 44)
And it is He Who made the Night and the Day to follow each other: for such as have the will to celebrate His praises or to show their gratitude. (Surah Al-Furqan, 62)
Please, click the following site for the full list of each verse mentioning day and light in Quran: https://www.quranindex.net/kelime.php?id=8511