The words chair, chare sound the same but have different meanings and spellings. Why do chair, chare sound the same even though they are completely different words?
The answer is simple: chair, chare are homophones of the English language.
A piece of furniture consisting of a seat, legs, back, and often arms, designed to accommodate one person.
A seat of office, authority, or dignity, such as that of a bishop.
An office or position of authority, such as a professorship.
A person who holds an office or a position of authority, such as one who presides over a meeting or administers a department of instruction at a college; a chairperson.
Alternative form of char (turn, task, chore, worker).
A narrow lane or passage between houses in a town.
To work by the day, without being a regularly hired servant; to do small jobs; to char.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").