mistake vs err

mistake is a noun but err is not a noun.

Word	Noun	Adjective	Verb	Adverb
mistake	Yes	No	Yes	No
err	No	No	Yes	No

As verbs, mistake and err are synonyms defined as:

Other synonyms of mistake include slip.

mistake (noun)	err (noun)
a wrong action attributable to bad judgment or ignorance or inattention
an understanding of something that is not correct
part of a statement that is not correct

mistake (verb)	err (verb)
to make a mistake or be incorrect	to make a mistake or be incorrect
identify incorrectly	wander from a direct course or at random