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 the debtor owes $1,000 to the bank, the $1,000 obligation is viewed as a debt by the debtor and as a claim by the bank.