The words boarder, border sound the same but have different meanings and spellings. Why do boarder, border sound the same even though they are completely different words?
The answer is simple: boarder, border are homophones of the English language.
One who boards, especially:
One who pays a stipulated sum in return for regular meals or for meals and lodging.
One who goes on board a vessel as part of an assault or military action: repel all boarders.
Sports A person who skis.
A part that forms the outer edge of something.
A decorative strip around the edge of something, such as fabric.
A strip of ground, as at the edge of a garden or walk, in which ornamental plants or shrubs are planted.
The line or frontier area separating political divisions or geographic regions; a boundary.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").