walking papers vs marching orders

walking papers and marching orders both are nouns.

Word	Noun	Adjective	Verb	Adverb
walking papers	Yes	No	No	No
marching orders	Yes	No	No	No

As nouns, walking papers and marching orders are synonyms defined as:

walking papers and marching orders: (informal) a notice of dismissal or discharge

walking papers (noun)	marching orders (noun)
(informal) a notice of dismissal or discharge	an order from a superior officer for troops to depart
	(informal) a notice of dismissal or discharge