The Arabic word nūr (Arabic: نور), associated with the moon, means the opposite of darkness in general. It can be a source of light, and it can be a reflection (or refraction for that matter) of light, too. None of the classical tafasīr (exegeses) of the Qur'an mentioned that the word nūr was used to denote the moon being a reflector of light. Any tafsīr that referred to the matter mentioned that the different words refer to the difference in the light's intensity rather than its source.
The word nūr is used in the Qur'an in connection with Allah ﷻ without likening Him to any of His creations:
اللَّهُ نُورُ السَّمَاوَاتِ وَالْأَرْضِ ۚ مَثَلُ نُورِهِ كَمِشْكَاةٍ فِيهَا مِصْبَاحٌ ۖ الْمِصْبَاحُ فِي زُجَاجَةٍ ۖ الزُّجَاجَةُ كَأَنَّهَا كَوْكَبٌ دُرِّيٌّ يُوقَدُ مِن شَجَرَةٍ مُّبَارَكَةٍ زَيْتُونَةٍ لَّا شَرْقِيَّةٍ وَلَا غَرْبِيَّةٍ يَكَادُ زَيْتُهَا يُضِيءُ وَلَوْ لَمْ تَمْسَسْهُ نَارٌ ۚ نُّورٌ عَلَىٰ نُورٍ ۗ يَهْدِي اللَّهُ لِنُورِهِ مَن يَشَاءُ ۚ وَيَضْرِبُ اللَّهُ الْأَمْثَالَ لِلنَّاسِ ۗ وَاللَّهُ بِكُلِّ شَيْءٍ عَلِيمٌ
Allah is the Light of the heavens and the earth. The example of His light is like a niche within which is a lamp, the lamp is within glass, the glass as if it were a pearly [white] star lit from [the oil of] a blessed olive tree, neither of the east nor of the west, whose oil would almost glow even if untouched by fire. Light upon light. Allah guides to His light whom He wills. And Allah presents examples for the people, and Allah is Knowing of all things.
— Surat An-Nur 24:35
In the verse above, there is no known scholarly opinion that restricts the word nūr therein to being a reflection. It is, however, commonly practiced in the Arabic language to use the word diyā' (Arabic: ضياء) to refer to a source of light and nūr to be the resulting light from said source. In the following verse, Allah ﷻ is giving an example of people who go astray to those who start a fire (istawqad, Arabic: استوقد) and as it radiates light (adā'at, Arabic: أضاءت), their light is taken away from them (nūrihim, Arabic: نورهم):
مَثَلُهُمْ كَمَثَلِ الَّذِي اسْتَوْقَدَ نَارًا فَلَمَّا أَضَاءَتْ مَا حَوْلَهُ ذَهَبَ اللَّهُ بِنُورِهِمْ وَتَرَكَهُمْ فِي ظُلُمَاتٍ لَّا يُبْصِرُونَ
Their example is that of one who kindled a fire, but when it illuminated what was around him, Allah took away their light and left them in darkness [so] they could not see.
— Surat Al-Baqarat 2:17
When examining the meaning of the word nūr in any of the Arabic-Arabic dictionaries at Al-Maany, one can see that the relevant translations refer to:
- shed light on
However, the Arabic word sirāj (Arabic: سراج) was only used in the Qur'an to refer to a source of light:
تَبَارَكَ الَّذِي جَعَلَ فِي السَّمَاءِ بُرُوجًا وَجَعَلَ فِيهَا سِرَاجًا وَقَمَرًا مُّنِيرًا
Blessed is He who has placed in the sky great stars and placed therein a [burning] lamp and luminous moon.
— Surat Al-Furqan 25:61
وَجَعَلَ الْقَمَرَ فِيهِنَّ نُورًا وَجَعَلَ الشَّمْسَ سِرَاجًا
And made the moon therein a [reflected] light and made the sun a burning lamp?
— Surat Nuh 71:16 (the verse you quoted in your question)
وَجَعَلْنَا سِرَاجًا وَهَّاجًا
And made [therein] a burning lamp
— Surat An-Naba 78:13
Likewise, the Arabic word diyā' (Arabic: ضياء) was only used in the Qur'an to refer to a source of light:
هُوَ الَّذِي جَعَلَ الشَّمْسَ ضِيَاءً وَالْقَمَرَ نُورًا وَقَدَّرَهُ مَنَازِلَ لِتَعْلَمُوا عَدَدَ السِّنِينَ وَالْحِسَابَ ۚ مَا خَلَقَ اللَّهُ ذَٰلِكَ إِلَّا بِالْحَقِّ ۚ يُفَصِّلُ الْآيَاتِ لِقَوْمٍ يَعْلَمُونَ
It is He who made the sun a shining light and the moon a derived light and determined for it phases - that you may know the number of years and account [of time]. Allah has not created this except in truth. He details the signs for a people who know
— Surat Yunus 10:5
قُلْ أَرَأَيْتُمْ إِن جَعَلَ اللَّهُ عَلَيْكُمُ اللَّيْلَ سَرْمَدًا إِلَىٰ يَوْمِ الْقِيَامَةِ مَنْ إِلَٰهٌ غَيْرُ اللَّهِ يَأْتِيكُم بِضِيَاءٍ ۖ أَفَلَا تَسْمَعُونَ
Say, "Have you considered: if Allah should make for you the night continuous until the Day of Resurrection, what deity other than Allah could bring you light? Then will you not hear?"
— Surat Al-Qasas 28:71
It is worth noting, though, that some modern tafasīr of the Qur'an explicitly say that the moon is not a source of light whereas the sun is a source of light when discussing Qur'an 71:16, for example, Āl Ghāzi al-'Āni in his book about the Qur'an:
وإنما سمى الأول نورا والآخر سراجا، لأن نور القمر منعكس عليه من الشمس لاختلاف تشكلاته بالقرب والبعد عنها
NOTE. My own translation, so treat with care.
And the former [moon] was called nūr and the latter [sun] was called sirāj because the light of the moon is a reflection from the sun that differs based on its proximity to the sun
— Bayān al-Ma'āni, Vol. 4, pp. 267 (Arabic only)
Some even elaborated about the topic by explicitly saying that the moon is intrinsically dark and that its luminance is the result of the reflection of sunlight, e.g., Ibn 'Ashūr in At-Tahrīr wa at-Tanwīr 30/204 (Arabic only) and
Sayyid Tantāwi in At-Tafsīr al-Waseet 15/119 (Arabic only).