milk shake vs eggshake

milk shake and eggshake both are nouns.

Word	Noun	Adjective	Verb	Adverb
milk shake	Yes	No	No	No
eggshake	Yes	No	No	No

As nouns, eggshake is a hyponym of milk shake; that is, eggshake is a word with a more specific, narrower meaning than milk shake:

milk shake: frothy drink of milk and flavoring and sometimes fruit or ice cream
eggshake: a milkshake with egg in it

Other hyponyms of milk shake include frappe, malt, malted, malted milk.

milk shake (noun)	eggshake (noun)
frothy drink of milk and flavoring and sometimes fruit or ice cream	a milkshake with egg in it