frappe vs milk shake

frappe and milk shake both are nouns.

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

As nouns, milk shake is a hypernym of frappe; that is, milk shake is a word with a broader meaning than frappe:

frappe: thick milkshake containing ice cream
milk shake: frothy drink of milk and flavoring and sometimes fruit or ice cream

Other hypernyms of frappe include milkshake, shake.

frappe (noun)	milk shake (noun)
a frozen dessert with fruit flavoring (especially one containing no milk)	frothy drink of milk and flavoring and sometimes fruit or ice cream
thick milkshake containing ice cream
liqueur poured over shaved ice