No, not in a practical sense. They are different terms for an obligation owed by the debtor to a creditor. A claim is the right of a creditor to the payment of an obligation by the debtor. A debt is a liability of a debtor on an obligation to a creditor. For example, if a debtor owes $1000 to the bank, the $1000 obligation is viewed as a debt by the debtor and as a claim by the bank.