By Imam Wahbah Az-Zuḥaylī, may Allah have mercy on him
Linguistically, ḍarūrah, as Al-Jurjānī has said in his Taʿrīfāt, is derived from the word ḍarar, and it is something that befalls one and cannot be repelled.
Terminologically, it has many approximate meanings, including what has been stated by Al-Jaṣāṣ, Abū Bakr Ar-Rāzī: ‘It is fear of harm or the destruction of oneself or some of one’s limbs as a result of not eating.’
There is also the expression of some contemporaries: ‘A ḍarūrah is more difficult to repel than a ḥājjah, for a ḍarūrah is that which if one goes against it the consequence is danger, such as being forced to seek refuge and fearing that one will die of starvation. It is not a condition that destruction be realised by refraining from that which is prohibited. Rather, it suffices that refraining would lead to unbearable weakness, or some harm to one’s health.’
The outward purport of this definition of ḍarūrah is heading towards the necessity of food and medicine, and other things can be analogically deduced from that. Its general rule is that it is everything that would lead to harm or danger to one’s person if one were to go against it, and so forth, and could possibly lead to destruction.
As for ḥājjah, it is more general than ḍarūrah, and it is that which if not responded to will lead to distress and difficulty, or some hardship or adversity that will not lead to destruction.
As for maṣlaḥah, it is the benefit that the Wise Lawgiver intends for His slaves by preserving their Dīn, their lives, their intellects, their lineage and their wealth according to a specific sequence that they have in relation to one another.
The difference between ḍarūrah and ḥājjah is from two angles:
The first is that ḍarūrah is based on an action that must be done in order for one to fulfill their responsibility, and a person simply can’t leave it off. As for ḥājjah, it is based on expansion and facilitation with regards to something that a person can leave off.
Thus, the furnishing of man’s needs falls under the category of ḍarūrah, such as clothing, shelter and refuge are from necessities (ḍarūrīyāt). Thus, the guardian of a minor must fulfill these needs for him, even if he has to sell real estate belonging to the minor. As for getting the minor married or teaching him, these merely fall under ḥājjah, and as a result of that, the Ḥānafīs hold that marrying off a young girl can only be done by means of the father or the grandfather and with a dowry that is similar to that of other women like her and she is married to someone who is suitable.
The second is that the exceptional rulings that are affirmed by ḍarūrah are by and large rulings of temporary permissibility for something that is forbidden and its prohibition in the Revealed Law is clear and text-based. As for the rulings that are based on ḥājjah, in most cases they do not contradict a clear text. Rather, most of the rulings of the Revealed Law that are found in their regard contradict analogy, due to them being based on ḥājjah. Thus, they contradict general principles as opposed to a text, and in most cases the ruling is fixed therein and it bears the attribute of permanence and constancy. The one in need benefits from it as well as others.
The rulings that are established for ḥājjah can be like the rulings that are established for ḍarūrah and thus temporarily permit something that is forbidden and contradict the forbidding text, such as instances of special ḥājjah that fall under the category of ḍarūrah.
[Translated from Qaḍāyā Al-Fiqh wa Al-Fikr Al-Muʿāṣir (Damascus: Dar Al-Fikr, 2008) v.2, p.100-101]
[This translation is now available from the English Naseem al-Sham site]
The Objectives of the Revealed Law
 (tn): i.e. harm
 Aḥkām Al-Qurʿān, 1/150 and what follows. See also Kashf Al-Asrār by Al-Bazdawī, 4/1518, Al-Qawānīn Al-Fiqhiyya by Ibn Juzay, p.173, Ash-Sharḥ Al-Kabīr by Ad-Dardīr, 2/115, Qawāʾid Az-Zarkashī (Al-Manthūr fī Tartīb Al-Qawāʾīd Al-Fiqhiyya) manuscript 137, no.8543, Al-Maktaba Az-Ẓāhiriyya in Damasus, Al-Mughnī 8/595, Mughnī Al-Muḥtāj 4/306
 (tn): i.e. death
 Al-Madkhāl Al-Fiqhī Al-ʿĀm by Ustādh, Ash-Sheikh Muṣṭafā Az-Zarqāʾ: f.600, 603
 Al-Maḥṣūl by Ar-Rāzī, p.194, and Al-Mustaṣfā by Al-Ghazāli, 1/139
 (tn): i.e. in the Book and Sunnah
 Ar. qiyās