doorway vs entree

doorway and entree both are nouns.

Word	Noun	Adjective	Verb	Adverb
doorway	Yes	No	No	No
entree	Yes	No	No	No

As nouns, entree is a hypernym of doorway; that is, entree is a word with a broader meaning than doorway:

doorway: the entrance (the space in a wall) through which you enter or leave a room or building; the space that a door can close
entree: something that provides access (to get in or get out)

Other hypernyms of doorway include entrance, entranceway, entry, entryway.

doorway (noun)	entree (noun)
the entrance (the space in a wall) through which you enter or leave a room or building; the space that a door can close	an entrance, especially a theatrical entrance onto a stage or as if onto a stage
	something that provides access (to get in or get out)
	the right to enter
	the principal dish of a meal