area vs plane section

area and plane section both are nouns.

Word	Noun	Adjective	Verb	Adverb
area	Yes	No	No	No
plane section	Yes	No	No	No

As nouns, plane section is a hyponym of area; that is, plane section is a word with a more specific, narrower meaning than area:

area: the extent of a 2-dimensional surface enclosed within a boundary
plane section: (geometry) the area created by a plane cutting through a solid

Other hyponyms of area include acreage, land area, footprint, erasure, blank space, place, space, space, balk, baulk, section.

area (noun)	plane section (noun)
a part of a structure having some specific characteristic or function	(geometry) the area created by a plane cutting through a solid
the extent of a 2-dimensional surface enclosed within a boundary
a part of an animal that has a special function or is supplied by a given artery or nerve
a subject of study
a particular geographical region of indefinite boundary (usually serving some special purpose or distinguished by its people or culture or geography)
a particular environment or walk of life