The essential point is that settlement applies to every matter and between every pair of contracting parties. As stated in the mursal hadith that has been accepted by the Ummah: “Settlement is permissible between Muslims”—that is, in every matter—and “permissible” here means legally effective—“except a settlement that makes lawful what is unlawful or makes unlawful what is lawful” (1); such a settlement is not legally effective.
Settlement has various forms. It may concern rights, property, or honor—indeed, anything. This is why Allah, Mighty and Majestic, states in general terms: “And settlement is best.” [al-Nisa' 4:128]
Here, in this chapter, the jurists mean settlement concerning property. They discuss settlement in disputes between a husband and his wife in the chapter on the treatment of wives, and under the chapter concerning those entitled to zakah, they discuss the indebted person who incurred a debt in order to reconcile people. Thus, each instance is addressed according to its particular context. What is meant here is settlement concerning property, and it is of two types: settlement based on acknowledgment and settlement based on denial. That is, settlement may concern something acknowledged by the person liable for the right, or something denied by the person liable for it.
The first is settlement based on acknowledgment. The author, may Allah have mercy on him, explained it in his statement: “If he acknowledges that he owes him a debt or a specific item, and the claimant remits or gives up part of it while retaining the remainder, it is valid.”