living space vs room

living space and room both are nouns.

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

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

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

Other hypernyms of living space include elbow room, way.

living space (noun)	room (noun)
space sought for occupation by a nation whose population is expanding	an area within a building enclosed by walls and floor and ceiling
	the people who are present in a room
	space for movement
	opportunity for

living space (verb)	room (verb)
	live and take one's meals at or in