بِسْمِ اللَّهِ الرَّحْمَـٰنِ الرَّحِيمِ
These two names express different aspects of mercy.
‘Al-Rahman’ being upon the wazn of fa3lan indicates the predominance of that quality as its being replete.
‘Al-Rahim’ being upon the wazn of fa3il indicates the repetitiveness of that quality as well as its occurrence on the intended object.
It is for this reason that some scholars said that Al-Rahman was a Name pointing to the Attribute of the Essence of Allah and ‘Al-Rahim’ was a Name pointing to the Attribute of Deed. According to Ibn Al-Qayyim: ‘Al-Rahman’ points to an Attribute that is existent in Him, and ‘Al-Rahim’ points to its interaction with the recipient of mercy. If you wish to understand this, ponder His saying,
وَڪَانَ بِٱلۡمُؤۡمِنِينَ رَحِيمً۬ا
(He is Most Merciful to the believers)
ٱلرَّحۡمَـٰنُ عَلَى ٱلۡعَرۡشِ ٱسۡتَوَىٰ
(The All-Merciful rose over the Throne)
for not once is it mentioned that he is Rahman with them.
Thus, Al-Rahman refers to One who is described with mercy, whereas Al-Rahim is One who shows mercy.
Extract from the eBook: The Spiritual Cure, An Explanation to Surah Al-Fatiha, prepared and translated by Abu Rumaysah. Very interesting book, you can download it here.