Plain and plane are easily confused in English – they are homophones, so you may write one when meaning the other. They have a number of distinct definitions where their meanings are completely different – but one meaning where their meanings are very similar, referring to flat empty space, where it can be hard to remember which word is correct.
Different meaning of plain and plane
The word plain usually has an adjective meaning, describing something as simple, easily evident, without adornment or without obstruction. For example a plain sweater (with no pattern) or to say “It was a plain to see.”, meaning clear/easily understood.
The word plane is usually used as a noun – most commonly an abbreviation of aeroplane / airplane, the flying vehicle. It can also refer to levels of achievements or to flat surfaces. A tool called a plane is used to create flat/smooth surfaces.
Where plain and plane can be confused
The confusion with plain and plane, however, comes from another specific meaning of plain, as a flat, empty area of land. For example, in the American West you have the Great Plains, vast expanses of flat land. This use is very similar to idea of a plane being a flat, level surface. So what is the difference?
A plain is very specifically an area of landscape – empty and flat, smooth, perhaps, but specifically a land formation.
A plane is more abstract – a concept of a flat, empty expanse that is not necessarily a physical landscape.
A plane can therefore refer to a mathematical or spiritual realm, something theoretical, while a plain refers to a physical place, something land-based.
This is an interesting word comparison for me, as I write fiction which often has both travelling and spiritual themes. In my fiction concerning the idea of the afterlife the word plane is often used to refer to a new spiritual area – “We have died and gone to another plane.” It is the theory of which world the characters inhabit. A plain would be used for something clearly physical – “They looked out at the dull plain before them.”