The words rappel, repel sound the same but have different meanings and spellings. Why do rappel, repel sound the same even though they are completely different words?
The answer is simple: rappel, repel are homophones of the English language.
A descent of a vertical surface, as a cliff or wall, by sliding down a belayed rope that is passed under one thigh and over the opposite shoulder or through a device that provides friction, typically while facing the surface and performing a series of short backward leaps to control the descent.
To descend from a steep height by this method.
The roll or beat of the drum to call soldiers to arms.
An ancient musical instrument, still used in Egypt, consisting of a ring to which are attached small bells or metal plates, forming a sort of rattle.
To ward off or keep away; drive back.
To offer resistance to; fight against.
To refuse to accept or submit to; reject.
To refuse to accept (someone); spurn.
Definitions from The American Heritage® Dictionary of the English Language, 5th Edition., from The Century Dictionary. 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").