In addition to retributive, a second category of suffering is discipline or chastisement. This is God allowing pain into the life of a believer for the purpose of spiritual growth. Though numerous verses move in this direction, some are especially pointed.
My son, do not despise the LORD’s discipline or be weary of his reproof, for the LORD reproves him whom he loves, as a father the son in whom he delights. (Prov. 3:11-12)
For the moment all discipline seems painful rather than pleasant, but later it yields the peaceful fruit of righteousness to those who have been trained by it. (Heb. 12:11)
Though the method of suffering may be similar, the key difference between these first two categories (retributive and discipline) is in God's motive. God punishes people to satisfy His wrath. He chastens believers to grow them in grace. In the first, God is moved by a righteous anger. In the latter, he is motivated by love.
In line with Proverbs 3:11-12, God's dealing with his children is always in love. As Christians, we believe that God satisfied his wrath against our sin at the cross. The Gospel teaches that Jesus exhausted the wrath of God for us (Rom. 8:1). More than an "atoning sacrifice" (NIV), Jesus is "the propitiation for our sins" (1 Jo. 2:2 ESV). Believing that God is punishing us with a retributive anger amounts a denial of the sufficiency of the Gospel (Heb. 7:25). This is not to say that God is unconcerned about our lifestyle. However, because we have been saved by grace, the Lord corrects us out of a motive of love, not wrath.
By way of application, I think it is extremely important for parents to make this differentiation when attempting to correct the behavior of their children. In our own home, my wife and I prefer the word "correct" or "discipline" to "punish." Punish implies a motive of anger, void of love. Discipline implies that the correction is out of love. I am not satisfying my wrath when I put my daughter in "time-out." I'm correcting her behavior because I love her. The grief she experiences in the time-out-chair is for her moral education, not for my personal satisfaction. We are also careful to communicate this to our children. I often ask my kids, "Does daddy love you more when you are good or when you are bad?" They know the answer to this one. With a smile and a chuckle I will hear, "Daddy, you love me all of the time." It's not that I am not grieved when one of my children sins, but they need to know that I love them as God loves me.