dash off vs write down

dash off and write down both are verbs.

Word	Noun	Adjective	Verb	Adverb
dash off	No	No	Yes	No
write down	No	No	Yes	No

As verbs, write down is a hypernym of dash off; that is, write down is a word with a broader meaning than dash off:

Other hypernyms of dash off include get down, put down, set down.

dash off (verb)	write down (verb)
write down hastily	reduce the estimated value of something
write quickly	put down in writing; of texts, musical compositions, etc.