Thanks very much for your question.
Presumptuous sins are those sins committed, I think, under the delusion that one is in fact doing the right thing. That is one presumes that one is, in fact, acting righteously but in reality one is actually engaged in sinful behaviour. So those who act in wrath and malice towards others with whom they disagree are acting presumptuously. The scribes and Pharisees and Sadducees are a good example. The Hebrew words translated presumption/presumptuously carry the connotation of pride and arrogance. One presumes one knows what's right without the need to consult God or His word and one acts accordingly. See Deuteronomy 1:43; 17:12,13; Psalm 19:13; 2 Peter2:10.
The difference therefore is one of attitude. Normally we sin when we are overcome by temptation or we inadvertently do something amiss. We sin presumptuously when we, in pride and arrogance, assume we know what's right and act without reference to God or His word. This is most serious because we are lulled into a false sense of complacency and can be unconscious of our hard-hearted and arrogant sinfulness. It often takes a "Road to Damascus" experience to dislodge us from such pride, arrogance, and folly, as it did with Saul of Tarsus.