Philosophy: Is the same offense and sin?

Bhaktivinod Thakur in Saranagati 2.7.3 (as well as in Jaiva dharma 8) distinguishes them.

sei saba päpa ära aparädha, ämi
parihäre päi lajjä, saba jäno' tumi

'By attempting to clear myself of all these sins and offenses I am put to shame. All this is surely understood by You.'

My understanding is that papa relates to material transgressions and aparadha to spiritual transgressions. But they are often confounded, as you say.