Both words can apply to a flat or level area. A plane is a more or less technical term for a flat surface: The sides of a pyramid rise on an inclined plane to meet at its apex; Joe tried to raise the level of conversation to a more elevated plane. A plain is a level tract of country: 'A gentle knight was pricking on the plain' (Spenser).
The ‘Sun of May’ was added in 1818. The blue bands are a shade known as ‘celeste’, said to be the colour of the sky which inspired Argentine revolutionary Manuel Belgrano before battle. Effective date: 16 August 1985.