PLAIN is an adverb which means, simple and ordinary looking, with no decorations.
It is also used as an adverb to emphasize upon something
As a noun, Plain is also used to define a large flat area, with fewer trees
She is wearing a plain dress.
I mean, you took the wrong way home, that’s plain stupid.
High mountains rise above the plain.
PLANE is a noun, commonly used to describe an airplane.
In mathematical terms, it is used to define a flat surface where a straight line joining two points can wholly lie.
The plane is flying high, above the sky.
Two planes intersect each other in a three-dimensional surface