dispatch vs write up

dispatch and write up both are nouns.

Word	Noun	Adjective	Verb	Adverb
dispatch	Yes	No	Yes	No
write up	Yes	No	Yes	No

As nouns, write up is a hypernym of dispatch; that is, write up is a word with a broader meaning than dispatch:

Other hypernyms of dispatch include account, news report, report, story.

dispatch (noun)	write up (noun)
the act of sending off something	a short account of the news
killing a person or animal
the property of being prompt and efficient
an official report (usually sent in haste)

dispatch (verb)	write up (verb)
kill without delay	bring to public notice by writing, with praise or condemnation
send away towards a designated goal	put into writing; write in complete form
complete or carry out
kill intentionally and with premeditation
dispose of rapidly and without delay and efficiently