plains / planes are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
plains: (noun) extensive tract of level open land.
planes: (noun) (mathematics) an unbounded two-dimensional shape. (noun) a level of existence or development. (noun) a power tool for smoothing or shaping wood. (noun) a carpenter's hand tool with an adjustable blade for smoothing or shaping wood. (verb) cut or remove with or as if with a plane. (verb) travel on the surface of water. (verb) make even or smooth, with or as with a carpenter's plane.
plains: p·l·EY·n·z
planes: p·l·EY·n·z
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)