neglect of duty vs carelessness

neglect of duty and carelessness both are nouns.

Word	Noun	Adjective	Verb	Adverb
neglect of duty	Yes	No	No	No
carelessness	Yes	No	No	No

As nouns, carelessness is a hypernym of neglect of duty; that is, carelessness is a word with a broader meaning than neglect of duty:

neglect of duty: (law) breach of a duty
carelessness: failure to act with the prudence that a reasonable person would exercise under the same circumstances

Other hypernyms of neglect of duty include neglect, negligence, nonperformance.

neglect of duty (noun)	carelessness (noun)
(law) breach of a duty	failure to act with the prudence that a reasonable person would exercise under the same circumstances
	the quality of not being careful or taking pains