For me as a native English speaker, it seems that compassionate and merciful differ slightly in meaning: we feel compassion when someone is suffering (the word literally means "suffering with") but we extend mercy when someone's own wrongdoing is the cause of their suffering. But they're closely linked and both Hebrew words are translated both ways. The same verse can be translated either way in different Bible versions.
I counted more than half a dozen times that rahûm was linked to the phrase, "slow to anger" (for example, in Psalm 103 vs 8) where the context clearly implies that God is being merciful in the face of people's sin and disobedience.
Etymologically, rahûm and raham are both derived from rehem - one of the Hebrew words for womb - suggesting that they describe the kind of tender affection a mother feels for her own child. This is borne out by Isaiah 49: 15, which says that God's compassion for us is even greater than a mother's feelings for her child.
God Himself proclaimed to Moses that He is merciful, gracious, compassionate, patient, loving and faithful. (Exodus 34: 6) Lamentations 3: 22 declares that, "His compassion never fails," or, "His mercies never come to an end." David enumerates exactly the same list of God's qualities in Psalm 86: 15.
When mercy and compassion appear in the same verse in English (it happens often in the psalms), usually one of the Hebrew words is rahûm or raham and the other is hesed - a word that's often translated in other places as "lovingkindness." And the Hebrew word hannûn (gracious) often appears in those same verses. That's the name I'll be reflecting on tomorrow.
While rahûm and raham most often seem to convey the sense of mercy/merciful in the Old Testament, the New Testament references to Jesus mostly convey the sense of compassion (usually the Greek word splagchnizomai). It's often used immediately before He heals someone who is sick or suffering: when healing two blind men in Matt 20: 34 or a leper in Mark 1: 41; when setting free the Gerasene demoniac in Mark 5: 19 or the demon-possessed boy in Mark 9: 22.
It's also used when He sees the bereaved widow of Nain weeping over the loss of her son (Luke 7: 13) and several times when He sees how lost the crowds are - like sheep without shepherd. In Mark 14: 14, His compassion led Him to heal the sick, and in Mark 6: 34, His compassion led Him to teach the crowds God's truth.
Splagchnizomai is also the word that Jesus chooses in Luke 15:20 to describe how the father felt on seeing his prodigal son returning. There it conveys both mercy for the son's misdeeds, as well as tender affection and compassion for the suffering the son had brought on himself.
So, the Old Testament tells us clearly that God is both merciful and compassionate, the gospels show us demonstrating that in person, and some of the New Testament letters also use the Greek words sympathēs and eusplagchnos when they urge us to show that same compassion to each other in brotherly love (for example, in 1 Peter 3: 8). We who've experienced God's mercy, should be the first to show mercy and compassion to others.
