figure of eight vs plane figure

figure of eight and plane figure both are nouns.

Word	Noun	Adjective	Verb	Adverb
figure of eight	Yes	No	No	No
plane figure	Yes	No	No	No

As nouns, plane figure is a hypernym of figure of eight; that is, plane figure is a word with a broader meaning than figure of eight:

figure of eight: a two-dimensional figure having the shape of the number eight
plane figure: a two-dimensional shape

Other hypernyms of figure of eight include two-dimensional figure.

figure of eight (noun)	plane figure (noun)
a knot having the shape of the numeral 8; tied in a rope that has been passed through a hole or pulley and that prevents the rope from coming loose	a two-dimensional shape
a two-dimensional figure having the shape of the number eight