Section Eight vs dismissal

Section Eight and dismissal both are nouns.

Word	Noun	Adjective	Verb	Adverb
Section Eight	Yes	No	No	No
dismissal	Yes	No	No	No

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

Section Eight: a discharge from the US Army based on unfitness or character traits deemed undesirable
dismissal: the termination of someone's employment (leaving them free to depart)

Other hypernyms of Section Eight include discharge, dismission, firing, liberation, release, sack, sacking.

Section Eight (noun)	dismissal (noun)
a discharge from the US Army based on unfitness or character traits deemed undesirable	the termination of someone's employment (leaving them free to depart)
a soldier who received a Section Eight discharge as unfit for military service	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