walking papers vs dismission

walking papers and dismission both are nouns.

Word	Noun	Adjective	Verb	Adverb
walking papers	Yes	No	No	No
dismission	Yes	No	No	No

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

Other hypernyms of walking papers include dismissal, pink slip.

walking papers (noun)	dismission (noun)
(informal) a notice of dismissal or discharge	the termination of someone's employment (leaving them free to depart)
	official notice that you have been fired from your job