✅ Answer: Please consider the following narrations:

1⃣عَنْ أَبِی بَصِیرٍ عَنْ أَبِی عَبْدِ اللَّهِ علیه السلام: فِی قَوْلِهِ الْحَمْدُ لِلَّهِ قَالَ الشُّکْرُ لِلَّهِ وَ فِی قَوْلِهِ رَبِّ الْعالَمِینَ قَالَ خَلَقَ الْمَخْلُوقِینَ الرَّحْمنِ بِجَمِیعِ خَلْقِهِ الرَّحِیمِ بِالْمُؤْمِنِینَ خَاصَّةً

📚 Tafsir al-Qummi, p. 26

Imam Sadiq (peace be upon him) said regarding the saying of Allah 'Alhamdulillah' that it means gratitude for Allah, and regarding 'Rabb al-'Alamin' that it means He created all creatures. 'Ar-Rahman' refers to Allah's mercy for all of His creation, while 'Ar-Rahim' refers specifically to His mercy towards the believers!

2⃣عَنْ عَبْدِ اللَّهِ بْنِ سِنَانٍ عَنْ أَبِی عَبْدِ اللَّهِ علیه السلام قَالَ: سَأَلْتُهُ عَنْ بِسْمِ اللَّهِ الرَّحْمنِ الرَّحِیمِ فَقَالَ الْبَاءُ بَهَاءُ اللَّهِ وَ السِّینُ سَنَاءُ اللَّهِ وَ الْمِیمُ مَجْدُ اللَّهَ وَ رَوَی بَعْضُهُمْ مُلْکُ اللَّهِ وَ اللَّهُ إِلَهُ کُلِّ شَیْءٍ الرَّحْمَنُ بِجَمِیعِ الْعَالَمِ وَ الرَّحِیمُ بِالْمُؤْمِنِینَ خَاصَّةً

📚 Ma'ani al-Akhbar, p. 3

Abdullah bin Sanan said: I asked Imam Sadiq (peace be upon him) about 'Bismillah ir-Rahman ir-Rahim'. He said: 'Bā' (ب) represents divine glory, 'Sīn' (س) represents divine splendor, and 'Mīm' (م) represents divine majesty. One narration mentions that 'Mīm' represents divine sovereignty, and Allah is the Lord of all things. 'Ar-Rahman' is for all the worlds, and 'Ar-Rahim' is for the believers specifically!

✅ 'Ar-Rahman' and 'Ar-Rahim' are two names derived from 'Ar-Rahmah' (mercy). Based on the above narrations, 'Ar-Rahman' signifies Allah’s mercy for all creation, while 'Ar-Rahim' signifies His special mercy for the believers.

✅ Some of Allah’s mercies are general and for all creatures, while others are exclusive to the believers. This concept is reflected in various verses and narrations:

📚 Bihar al-Anwar, Vol. 72, p. 52

3⃣عَنْ حُمْرَانَ عَنْ أَبِی جَعْفَرٍ علیه السلام قَالَ : إِنَّ هَذِهِ الدُّنْیَا یُعْطَاهَا الْبَرُّ وَ الْفَاجِرُ وَ إِنَّ هَذَا الدِّینَ دِینٌ لَا یُعْطِیهِ اللَّهُ إِلَّا خَاصَّتَهُ.

Imam Baqir (peace be upon him) said: Indeed, this world is given both to the righteous and to the wicked, but this religion is given only to Allah's special and chosen ones!

📚 Bihar al-Anwar, Vol. 72, p. 52

4⃣عَنْ مُحَمَّدِ بْنِ مُسْلِمٍ عَنْ أَبِی جَعْفَرٍ علیه السلام قَالَ: إِنَّ اللَّهَ لَیُعْطِی الدُّنْیَا مَنْ یُحِبُّ وَ یُبْغِضُ وَ لَا یُعْطِی الْآخِرَةَ إِلَّا مَنْ یُحِبُّ وَ إِنَّ الْمُؤْمِنَ لَیَسْأَلُ رَبَّهُ مَوْضِعَ سَوْطٍ فِی الدُّنْیَا فَلَا یُعْطِیهِ وَ یَسْأَلُهُ الْآخِرَةَ فَیُعْطِیهِ مَا شَاءَ وَ یُعْطِی الْکَافِرَ فِی الدُّنْیَا قَبْلَ أَنْ یَسْأَلَهُ مَا شَاءَ وَ یَسْأَلُهُ مَوْضِعَ سَوْطٍ فِی الْآخِرَةِ فَلَا یُعْطِیهِ شَیْئاً.

Imam Baqir (peace be upon him) said: Surely, Allah grants the world to those whom He loves and to those whom He dislikes, but He does not grant the Hereafter except to those whom He loves! A believer asks for a small amount in this world, as much as a place for a lash, but Allah does not grant it to him. However, when he asks for the Hereafter, He gives him what he asks for! A disbeliever, before even asking, is given whatever he wants in this world, but when he asks for the Hereafter, as much as a place for a lash, it is not granted to him!

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اللَّهُمَّ صَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْر