This is fairly basic but it is easy to type or write the wrong word when you are in a hurry. I tend to find that plane is used in place of plain. I haven’t yet seen an aircraft referred to as a ‘plain’.

Plain

• without decoration or adornment
• without pattern or with one colour or with simple weave (when a fabric)
• having no particular beauty
• flat or smooth
• easily understood; clear or simple; unequivocal
• a lowly person or lowly people (usually in social rank or education)
• a simple stitch in knitting
• to mourn, lament or complain

Plane

• an aeroplane
• to glide, skim or soar without moving wings
• a level surface; level or flat
• a flat surface on which a straight line joining any two points on it lies entirely on that surface
• a level of existence, thought or attainment
• a tool with a block and projecting steel blade for smoothing timber or wooden surfaces; to smooth timber or remove material using a plane
• a type of tall spreading tree