The words bait, bate sound the same but have different meanings and spellings. Why do bait, bate sound the same even though they are completely different words?
The answer is simple: bait, bate are homophones of the English language.
Food or other lure placed on a hook or in a trap and used in the taking of fish, birds, or other animals.
Something, such as a worm, used for this purpose.
An enticement; a temptation.
Archaic A stop for food or rest during a trip.
To lessen the force or intensity of; moderate: "To his dying day he bated his breath a little when he told the story” ( George Eliot). See Usage Note at bait1.
To take away; subtract.
To flap the wings wildly or frantically. Used of a falcon.
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").