Debt: a payment or delivery obligation rests upon the person making the admission; the inquiry is how it must be discharged.
Trust: another person's specific property is held by the speaker; the inquiry is its return and the custodian's duties.
Both acknowledge a right against the speaker in a legally relevant sense. They differ in the nature of the right, not in whether the other person has any right.
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Debt versus trust: a focused comparison
Kitab al-Iqrar: Debt and Trust, Admissions by Reply, and Deferred Debts
Debt: a payment or delivery obligation rests upon the person making the admission; the inquiry is how it must be discharged.
Trust: another person's specific property is held by the speaker; the inquiry is its return and the custodian's duties.
Both acknowledge a right against the speaker in a legally relevant sense. They differ in the nature of the right, not in whether the other person has any right.