opheiletēs

This is the plain commercial meaning, and outside the Bible it is the only one the Greek world knew. In contracts, loan receipts, and tax records the word simply labels the party who has not yet paid. Greek also had a blunter compound reserved for money alone, used of the two men who owed a lender in one of Jesus's stories (χρεωφειλέτης).

The New Testament keeps this sense in one place and puts it to work. In the story of the unforgiving servant, a man is brought in who owes ten thousand talents. The figure is not a plausible sum; it is a joke about scale, more than ten times the yearly income of Herod's whole kingdom. His master cancels it outright, and the servant then refuses to release a fellow servant who owes him about a hundred days' wages.

Because that debt is cancelled by a king and stands for a sum no one could ever repay, even this ordinary business use of the word is doing more than accounting.

Ordinary Greek used the word this way long before the New Testament: a person could be a debtor of a favor as easily as of money, and the same word covered being bound to carry out a duty. Paul uses it four times, always in this sense, never for sin.

What changes in Paul is what the debt is made of. He calls himself a debtor to Greeks and to those outside Greek culture, meaning that the commission he was given leaves him owing them the message he carries. He tells the Roman Christians they are debtors, but not to their old selves, and then breaks off without finishing the thought. He describes the churches in Greece as debtors to Jerusalem, since they received something spiritual from there and now owe something material back. In each case a gift already received is what creates the obligation, which is exactly how favor and duty worked in the wider culture of the day.

Galatians turns the picture around. There, taking on circumcision as a way of being right with God makes a person a debtor to keep the whole law, every part of it, with nothing left optional. It is the one place where being a debtor is a warning rather than a privilege.

This is the sense with no parallel in ordinary Greek. It comes from Aramaic, the everyday language Jesus spoke, where one word covered both an unpaid bill and a moral wrong, and where the person so described might be a man who owed money or a man who was guilty and liable to punishment. Older Hebrew had pictured wrongdoing differently, as a weight a person carries on his back (עָוֹן). By the time of Jesus the accounting picture had largely taken over.

So when the Lord's Prayer asks God to cancel our debts as we cancel the debts of the people who owe us, it is asking for the forgiveness of sins. Matthew shows that this is what he means: two verses later he restates the same petition using an ordinary word for wrongs done. Luke, writing for readers who would hear only money in the word, half translates it, putting "sins" in the first half of the line and leaving the language of owing in the second.

Luke uses the word the same way in a scene about disaster. Jesus asks whether eighteen people killed when a tower collapsed were worse debtors than everyone else in the city. Two verses earlier he had called another group plainly sinners (ἁμαρτωλός), and the switch between the two words shows they carry the same force here. Modern translations give up on "debtors" in that verse and print "offenders" or "more guilty" instead.