The words rain, reign, rein sound the same but have different meanings and spellings. Why do rain, reign, rein sound the same even though they are completely different words?
The answer is simple: rain, reign, rein are homophones of the English language.
A fall of such water; a rainstorm.
The descent of such water.
Water condensed from atmospheric vapor and falling in drops.
Rainy weather.
To be predominant or prevalent: Panic reigned as the fire spread.
Exercise of sovereign power, as by a monarch.
The period during which a monarch rules.
Dominance or widespread influence: the reign of reason.
A long narrow leather strap attached to each end of the bit of a bridle and used by a rider or driver to control a horse or other animal. Often used in the plural.
A means of restraint, check, or guidance.
A means or an instrument by which power is exercised. Often used in the plural: the reins of government.
To check or hold back by or as if by the use of reins. Often with in, back, or up.
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").