I think the trespasses/debts/sins really just depends on how the prayer is translated into English.
Think about how many Bible translations there are - you can take 3 translations, look up the Greek word, and find it translated in 3 ways.
When I hear "trespasses" I think of one of those "NO TRESPASSING" signs you will find stapled to trees in rural areas.
And with debts, I think of my college loans
So when I say the prayer I usually say "sins," it makes the most sense to me. I think "debt" and "trespass" are more archaic forms. Just guessing though.