marching orders vs dismission

marching orders and dismission both are nouns.

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

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

Other hypernyms of marching orders include dismissal, pink slip.

marching orders (noun)	dismission (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	official notice that you have been fired from your job