The meaning of the Most Gracious, the Most Merciful
The Most Gracious and the Most Merciful are two attributes of Allah Almighty, and they signify the mercy of Allah. But the Most Gracious (Alrahman) is employed only when we are referring to Allah, it has the same attribute of the word Allah, and the two words Allah and Alrahman altogether have been mentioned in Surat Alisraa Aya (110) where Allah says: "Say Call upon Allah or Call upon the Most Gracious, whichever you call, to Him belong the Most Beautiful Names".
So Allah says call upon Him by the Name Allah or the Name Alrahman, whichsoever name you like all names belong to the One, so if you call upon Him by Allah, He is so, and if you call upon Him by the Most Gracious, He is so. Thereupon, among all beautiful Names of Allah only the Name Allah and the Name Alrahman are exclusive to the One, and it is not permissible to qualify anyone besides Allah by the two attributes.
In addition to that, there is a full Surah of the Holy Quran is called Surat Alrahman (the Most Gracious), and it started with the word Alrahman, then Allah describes Alrahman by saying: He taught the Quran, He created the human being, and He taught him distinct speech (how to express himself), then Allah recounted his favor and his bounties all over the Surah, and after each bounty Allah asked them: so which of the favor (bounties) of your lord would you deny?.
Although the Name Alrahman (The Most Gracious) is exclusive to Allah, Almighty, but the Name Raheem (Merciful) is not the same; For Allah has described His Messenger Muhammad (PBUH) with the attribute Raheem as He says in Surat Altawbah Aya (128) {There has certainly come to you a Messenger from among yourselves, Grievous to Him is what you suffered, Keen on you, and to the believers is kind, merciful}.
The attribute Alraheem conveys a glad tidings of the mercy of Allah Almighty to the believers, as Allah says in Aya (43) of Surat Alahzab {It is He who sends blessings upon you and His Angels, so that He may bring you out of the darknesses to light, and He is Most-Merciful to the believers}.
Thus, there is a broader scope of the attribute the Most Gracious (Alrahman) than the attribute the Most Merciful (Alraheem); Alrahman shows Allah's mercy to His creations, and the attribute Alraheem (Most Merciful) is exclusive to the believers. Allah described Himself and His Messenger (PBUH) with mercy to the believers, and Allah's Mercy is not only in the worldly life by showing them the right path and bringing them out of the darkness to the light, but it is also in the Hereafter by saving them on the day of resurrection.
