Difference between inculpate and incriminate?

Inculpate, to all intents and purposes, became rare (save in formal legal writing) around the late 19th century when incriminate took over from it. Rhetorically, inculpate is usually used in the context of a contrast to exculpate. See Google Ngrams for inculpate, incriminate

The OED gives

Inculpate: 1. transitive. To bring a charge against; to accuse; to blame, find fault with.

1799 S. Turner Hist. Anglo-Saxons I. iii. iii. 173 Gildas inculpates him for having destroyed his uncle.

in which inculpate can be used, as shown, as a close synonym for blame, accuse or find fault with [someone]:

To incriminate lacks this meaning.