wrongdoing vs activity

wrongdoing and activity both are nouns.

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

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

wrongdoing (noun)	activity (noun)
activity that transgresses moral or civil law	any specific behavior
departure from what is ethically acceptable	the trait of being active; moving or acting rapidly and energetically
	an organic process that takes place in the body
	a process existing in or produced by nature (rather than by the intent of human beings)
	the state of being active
	(chemistry) the capacity of a substance to take part in a chemical reaction