The words bair, bare, bear sound the same but have different meanings and spellings. Why do bair, bare, bear sound the same even though they are completely different words?
The answer is simple: bair, bare, bear 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.
Archaic A past tense of bear1.
Lacking the usual or appropriate covering or clothing; naked: a bare arm.
Exposed to view; undisguised: bare fangs.
Lacking the usual furnishings, equipment, or decoration: bare walls.
To hold up; support.
To carry from one place to another; transport.
To carry in the mind; harbor: bear a grudge.
To transmit at large; relate: bearing glad tidings.
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").