dinner dress vs evening dress

dinner dress and evening dress both are nouns.

Word	Noun	Adjective	Verb	Adverb
dinner dress	Yes	No	No	No
evening dress	Yes	No	No	No

As nouns, evening dress is a hypernym of dinner dress; that is, evening dress is a word with a broader meaning than dinner dress:

Other hypernyms of dinner dress include evening clothes, eveningwear, formalwear, gown.

dinner dress (noun)	evening dress (noun)
a gown for evening wear	attire to wear on formal occasions in the evening