In the Quran, Allaah mentioned His Rahmah (mercy) in many places. In another place, He mentioned Prophet Mohamed, sallallaahu 'alayhi wa sallam, as "Rahmah Lil’aalameen". Are these two Rahmahs the same?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.

Allaah, The Almighty, described Himself with Mercy. Allaah says (what means): {Your Lord is the possessor of vast mercy.} [Quran 6:147]

Allaah assigned a portion of His Mercy on the earth by which the creatures are merciful to each other, such as the mercy which Allaah had put in the hearts of the mothers. Abu Hurayrah narrated that the Prophet said, “Allaah has one hundred mercies, from which He descended one mercy between the jinn, human beings, animals, and vermin, by which they are compassionate and merciful to each other and by which a wild animal is compassionate to its young.” [Muslim]

Also, Allaah had sent His Prophet and made him a mercy and a blessing from Him to this nation. So the mercy of the Prophet is from the mercy of Allaah, and Allaah is Merciful to the ’Aalameen (all worlds) with his Prophet; as Allaah says (what means): {And We have not sent you [O Muhammad ] except as a mercy to the worlds.} [Quran 21:107]

Al-Mustadrak ‘ala As-Saheehayn, authored by Al-Haakim, reads, "Abu Hurayrah narrated that the Prophet said, "O people, I am but a gift of mercy." (Al-Haakim said, 'This is a saheeh (sound) hadeeth on the criteria set out by Al-Bukhari and Muslim.' Ath-Thahabi and Al-Albaani agreed with Al-Haakim.

Besides, Abu Hurayrah narrated, “The people said, 'O Messenger of Allaah, supplicate against the polytheists.' He said, 'I was not sent as a curser; rather, I was sent as a mercy.'” [Muslim]

Allaah knows best.