living space vs elbow room

living space and elbow room both are nouns.

Word	Noun	Adjective	Verb	Adverb
living space	Yes	No	No	No
elbow room	Yes	No	No	No

As nouns, elbow room is a hypernym of living space; that is, elbow room is a word with a broader meaning than living space:

living space: space sought for occupation by a nation whose population is expanding
elbow room: space for movement

Other hypernyms of living space include room, way.

living space (noun)	elbow room (noun)
space sought for occupation by a nation whose population is expanding	space for movement