The words whicker, wicker sound the same but have different meanings and spellings. Why do whicker, wicker sound the same even though they are completely different words?
The answer is simple: whicker, wicker are homophones of the English language.
To whinny.
A whinny.
A flexible plant branch or twig, as of a willow, used in weaving baskets or furniture.
Wickerwork.
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").