The words miner, minor sound the same but have different meanings and spellings. Why do miner, minor sound the same even though they are completely different words?
The answer is simple: miner, minor are homophones of the English language.
One whose work or business it is to extract ore or minerals from the earth.
A machine for the automatic extraction of minerals, especially of coal.
A soldier, often a specialist, engaged in mining operations.
Zoology A leaf miner.
Lesser or smaller in amount, extent, or size.
Lesser in importance, rank, or stature: a minor politician.
Lesser in seriousness or danger: a minor injury.
Law Being under legal age; not yet a legal adult.
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").