marching orders vs walking papers

marching orders and walking papers both are nouns.

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

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

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

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