I don't think the difference really translates to English. Actually most Arabs don't really understand the difference. Supposedly, "Rahman" is a more exaggerated from of "Raheem", and both basically mean "merciful".

No, they both have meaning in English. In the Quran before we start reading or reciting any of the words of the Quran we start by saying "Bism Ellah Al Rahman Al Raheem. This literally means: "in the name of Allah (God) the most gracias and most merciful." Therfore, "Rahman" is gracias and "Raheem" is merciful.

all of which indicate that God is merciful Rahman = indicates the magnitude of God's mercy Raheem = refers to the mercy of God that reaches all of creation. ...

Both derived from rahmah = mercy رحمة but rahman is Noun and special name to the almighty Allah SWT. and you cannot say that this or that person rahman, there is only one Rahman and we are his slaves. But raheem is an adjective derived from the same word rhamah رحمة this is shared and common , you can call the one who show mercy with others as raheem , and people who "mercy" others as رحماء.