The words altar, alter sound the same but have different meanings and spellings. Why do altar, alter sound the same even though they are completely different words?
The answer is simple: altar, alter are homophones of the English language.
An elevated place or structure before which religious ceremonies may be enacted or upon which sacrifices may be offered.
A structure, typically a table, before which the divine offices are recited and upon which the Eucharist is celebrated in Christian churches.
To change or make different; modify: altered my will.
To adjust (a garment) for a better fit.
To castrate or spay (an animal, such as a cat or a dog).
To change or become different.
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").