New Defender's Study Bible Notes
7:10 godly sorrow. Instead of provoking resentment against Paul by the Corinthians, whom he had rather severely censured in that letter, Paul’s first letter had actually produced sorrow for their sins—“godly sorrow,” that is, of sorrow from God—leading to true repentance and correction of the sin which had been particularly rebuked (I Corinthians 5:1-6; note verse 6, also II Corinthians 2:1-10). This response proved the genuineness of their salvation.
7:10 sorrow of the world. The “sorrow of the world,” on the other hand, is not sorrow for the sin itself, but sorrow over its consequences (e.g., Luke 13:27-28). This type of sorrow issues only in eternal death, not salvation.
7:11 carefulness. That is, “anxiety.”