The words rote, wrote sound the same but have different meanings and spellings. Why do rote, wrote sound the same even though they are completely different words?
The answer is simple: rote, wrote are homophones of the English language.
A memorizing process using routine or repetition, often without full attention or comprehension: learn by rote.
The sound of surf breaking on the shore.
A medieval stringed instrument variably identified with a lyre, lute, or harp.
Past tense of write.
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.