marching orders vs dismissal

marching orders and dismissal both are nouns.

Word	Noun	Adjective	Verb	Adverb
marching orders	Yes	No	No	No
dismissal	Yes	No	No	No

As nouns, dismissal is a hypernym of marching orders; that is, dismissal is a word with a broader meaning than marching orders:

Other hypernyms of marching orders include dismission, pink slip.

marching orders (noun)	dismissal (noun)
an order from a superior officer for troops to depart	the termination of someone's employment (leaving them free to depart)
(informal) a notice of dismissal or discharge	a judgment disposing of the matter without a trial
	official notice that you have been fired from your job
	permission to go; the sending away of someone