birthday vs day of remembrance

birthday and day of remembrance both are nouns.

Word	Noun	Adjective	Verb	Adverb
birthday	Yes	No	No	No
day of remembrance	Yes	No	No	No

As nouns, day of remembrance is a hypernym of birthday; that is, day of remembrance is a word with a broader meaning than birthday:

birthday: an anniversary of the day on which a person was born (or the celebration of it)
day of remembrance: the date on which an event occurred in some previous year (or the celebration of it)

Other hypernyms of birthday include anniversary.

birthday (noun)	day of remembrance (noun)
an anniversary of the day on which a person was born (or the celebration of it)	the date on which an event occurred in some previous year (or the celebration of it)
the date on which a person was born