The words war, wore sound the same but have different meanings and spellings. Why do war, wore sound the same even though they are completely different words?
The answer is simple: war, wore are homophones of the English language.
A state of open, armed, often prolonged conflict carried on between nations, states, or parties.
The period of such conflict.
The techniques and procedures of war; military science.
A condition of active antagonism or contention: a war of words; a price war.
Past tense of wear.
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").