The words cere, sear, seer, sere sound the same but have different meanings and spellings. Why do cere, sear, seer, sere sound the same even though they are completely different words?
The answer is simple: cere, sear, seer, sere are homophones of the English language.
To wrap in or as if in cerecloth.
A fleshy or waxlike membrane at the base of the upper beak in certain birds, such as parrots, through which the nostrils open.
To char, scorch, or burn the surface of with or as if with a hot instrument. See Synonyms at burn1.
To cause to dry up and wither.
To become withered or dried up.
A condition, such as a scar, produced by searing.
One that sees: an inveterate seer of sights.
Withered; dry: sere vegetation at the edge of the desert.
The entire sequence of ecological communities successively occupying an area from the initial stage to the climax.
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").