Some Christians pray the Lord’s Prayer using the word “trespasses,” while others use the words “debts” or “sins.” The Greek word paraoptomata means “trespasses,” while opheilemata means “debts” and hamartias means “sins.” Matthew and Luke both use any one of those words in various manuscripts. The more important word in the prayer is aphiemi which means “forgive.” The concept that Christ is communicating is that we are to “forgive,” whether debts, trespasses, or sins.
One of the reasons “trespasses” has been used by so many for so long is that forgiving a debt, while a charitable deed, is different from forgiving an offense (trespass). Theologically, it is better to restrict the word “sin” to an offense against God since it involves putting one’s own will against the Divine Will. If I put my will against your will, it is not necessarily sinful. If you owe me money and I dissolve the debt, there is no real forgiveness as is demanded by the Gospel.
Forgiveness is to pardon someone who offended, hurt, or attacked us. It implies there is guilt in the offender, regardless of whether or not there is repentance, sorrow, or contrition. We can forgive those who have not even asked for our forgiveness. We are asked to forgive our enemies, to love them, and to pray for them.
Using “trespasses” in the Lord’s Prayer in this context, then, seems to make more sense than using “debts” or “debtors,” but all three (sins, debts, and trespasses) are found in the Gospel nonetheless.