despatch vs write up

despatch and write up both are nouns.

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

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

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

despatch (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)

despatch (verb)	write up (verb)
send away towards a designated goal	bring to public notice by writing, with praise or condemnation
	put into writing; write in complete form