A group of commentators understand RAHMÄN, (TRANSLATED MERCIFUL) to mean and denote Allah's common Mercy, that covers all
His creatures, whether a friend or enemy; a faithful, or a heathen - all and all.
As for the other derivative name RAHIM, (TRANSLATED COMPASSIONATE) reveals Allah's SPECIAL MERCY and favour, which is dedicated to His obedient and faithful servants.
Here, a point worthy of note is that: Throughout the HOLY QURÄN, the word RAHMÄN is used in ABSOLUTE MODE to mean unlimited and unrestricted, thus showing the commonness of the word; but RAHIM is used especifically which denotes being bound to its peculiarity.