The words armer, armor sound the same but have different meanings and spellings. Why do armer, armor sound the same even though they are completely different words?
The answer is simple: armer, armor are homophones of the English language.
One who arms or supplies with arms; one who equips.
A defensive covering, as of metal, wood, or leather, worn to protect the body against weapons.
A tough, protective covering, such as the bony scales covering certain animals or the metallic plates on tanks or warships.
A safeguard or protection: faith, the missionary's armor.
The combat arm that deploys armored vehicles, such as tanks.
Definitions from The Century Dictionary and Cyclopedia, 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.