The words crape, crepe sound the same but have different meanings and spellings. Why do crape, crepe sound the same even though they are completely different words?
The answer is simple: crape, crepe are homophones of the English language.
A black band worn, as on the sleeve, as a sign of mourning. Also called crepe.
To cover or drape with or as if with crape.
A light soft thin fabric of silk, cotton, wool, or another fiber, with a crinkled surface. Also called crape.
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.