door vs admittance

door and admittance both are nouns.

Word	Noun	Adjective	Verb	Adverb
door	Yes	No	No	No
admittance	Yes	No	No	No

As nouns, admittance is a hypernym of door; that is, admittance is a word with a broader meaning than door:

Other hypernyms of door include access, accession, admission, entree.

door (noun)	admittance (noun)
a swinging or sliding barrier that will close the entrance to a room or building or vehicle	the act of admitting someone to enter
the entrance (the space in a wall) through which you enter or leave a room or building; the space that a door can close	the right to enter
a room that is entered via a door
a structure where people live or work (usually ordered along a street or road)
anything providing a means of access (or escape)