What is the difference between Rahmah, Rizq, and the Fadhl of Allah?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.

Linguistically speaking, Rahmah means mercy, compassion, and kindness. Ibn Al-Qayyim said, “Rahmah means mercy and compassion ...” [Badaa‘i’ As-Fawaa'id]

The mercy of Allah, the Exalted, for His slaves means His kindness and compassion for them.

Rizq means provision or sustenance. It originally means ‘Ataa’ (that which is given). Lisaan Al-ʻArab defines it as follows, “Rizq denotes whatever is of benefit. Plural: Arzaaq. Rizq is whatever is given; as in saying: Allah gave so-and-so Rizq.” Allah says (what means): {Eat and drink from the Rizq (provision) of Allah ...} [Quran 2:60] The Rizq of Allah in the verse refers to what He gave them (the Israelites) of Mann (manna), Salwa (quails), and water.

Fadhl originally means surplus and abundant good.

Ibn Faaris said, “Fadhl means surplus and (what is) good.” [Maqayees Al-Lughah]

Ar-Raaghib said, “Fadhl means what is in excess beyond frugality.” [Al-Mufradaat]

Thus, the Fadhl of Allah means the good which He bestows on His creation. Likewise, it denotes what is given out of grace and favor without reason. Taaj Al-ʻAroos reads, “Everything that is given without the obligation of giving it to the recipient is called Fadhl. This meaning is reflected in the following verses: Allah, the Exalted, says (what means): {And ask Allah of his Fadhl (bounty).} [Quran 4:32] {That is the Fadhl (bounty) of Allah, which He gives to whom He wills...} [Quran 62:4]”

Allah knows best.