The words dike, dyke sound the same but have different meanings and spellings. Why do dike, dyke sound the same even though they are completely different words?
The answer is simple: dike, dyke are homophones of the English language.
An embankment of earth and rock built to prevent floods.
Chiefly British A low wall, often of sod, dividing or enclosing lands.
A barrier blocking a passage, especially for protection.
A raised causeway.
Variant of dike1.
Offensive Slang Used as a disparaging term for a lesbian.
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").