transgression vs wrongdoing

transgression and wrongdoing both are nouns.

Word	Noun	Adjective	Verb	Adverb
transgression	Yes	No	No	No
wrongdoing	Yes	No	No	No

As nouns, wrongdoing is a hypernym of transgression; that is, wrongdoing is a word with a broader meaning than transgression:

transgression: the act of transgressing; the violation of a law or a duty or moral principle
wrongdoing: activity that transgresses moral or civil law

Other hypernyms of transgression include actus reus, misconduct, wrongful conduct.

transgression (noun)	wrongdoing (noun)
the act of transgressing; the violation of a law or a duty or moral principle	activity that transgresses moral or civil law
the action of going beyond or overstepping some boundary or limit	departure from what is ethically acceptable
the spreading of the sea over land as evidenced by the deposition of marine strata over terrestrial strata