It is a general attribute that encompasses the creation of the deficient. The name Allah is general, while al-Raḥmān is specific. That is, the name al-Raḥmān (the All-Merciful) is, in a particular sense, exclusive to Him alone by virtue of divine perfections, whereas the name Allah applies both to the Real (al-Ḥaqq) and to creation (the created beings).
When the name al-Raḥmān is assigned to one of the perfections (kamālāt), its meaning is referred to the name that is most fitting for that perfection in its own locus, as is the case with the names Rabb (Lord), Malik (King), and others. The meanings of all these names, unlike the name al-Raḥmān, are restricted to the meaning appropriate to the rank to which they are ascribed. The concept of the name al-Raḥmān, however, is that, while it itself possesses perfection, it also encompasses all the attributes of perfection. In other words, al-Raḥmān is an attribute that includes all divine attributes. (al-Insān 76:20)
The word al-Raḥmān is a word on the faʿlān morphological pattern, and its lexical meaning is that the one possessing this attribute must be powerful and manifest in it. For this reason, His mercy has encompassed all things. So much so that even the state of the people of Hell has (almost) turned to mercy. Know that all the divine essential names are subsumed under this name. These are seven: life, knowledge, qudra (power), will, hearing, sight, and kalām (speech). (al-Insān 76:22)
Raḥīm and Raḥmān are two names derived from the root of mercy (raḥma). However, al-Raḥmān is general, whereas al-Raḥīm is more specific and complete. The generality of al-Raḥmān is due to its encompassing all existents, while the specificity of al-Raḥīm is because it pertains only to the people of felicity.
The mercy of al-Raḥmān is intermingled with unpleasantness, just as, even though it is mercy for the sick, drinking a medicine that tastes and smells unpleasant is required. There are some things in this that nature dislikes. The mercy of al-Raḥīm is not like this; in it, there is no taint or anything disliked—it is pure blessing. This is a blessing that only those of complete felicity can attain. This blessing, the mercy that arises under the attribute of al-Raḥīm, is the manifestation and effect of Allah's mercy in His names and attributes.
Raḥmāniyya (the quality of al-Raḥmān)—al-Raḥīm within al-Raḥmān is like the eye within the human body. One of them is more specific, more precious, and more important; the other gathers all of them within itself. For this reason, it has been said that the mercy of al-Raḥīm can only be seen in its fullness in the Hereafter, because it is broader than the world (dunyā). In the world, every blessing is mixed with some turbidity, and this is among the manifestations of al-Raḥmān. (al-Insān I, 28)
The name Rabb is authorized from the name al-Raḥīm, the name al-Raḥīm is authorized from the name al-Raḥmān, the name al-Raḥmān is authorized from the name Allah, and the name Allah is authorized from the Essence (Dhāt). (Nafahāt, 62)