ID vs badge

ID and badge both are nouns.

Word	Noun	Adjective	Verb	Adverb
ID	Yes	No	No	No
badge	Yes	No	Yes	No

As nouns, badge is a hypernym of ID; that is, badge is a word with a broader meaning than ID:

ID: a card or badge used to identify the bearer
badge: an emblem (a small piece of plastic or cloth or metal) that signifies your status (rank or membership or affiliation etc.)

Other hypernyms of ID include positive identification.

ID (noun)	badge (noun)
a card or badge used to identify the bearer	any feature that is regarded as a sign of status (a particular power or quality or rank)
a state in the Rocky Mountains	an emblem (a small piece of plastic or cloth or metal) that signifies your status (rank or membership or affiliation etc.)

ID (verb)	badge (verb)
	put a badge on