The words capital, capitol sound the same but have different meanings and spellings. Why do capital, capitol sound the same even though they are completely different words?
The answer is simple: capital, capitol are homophones of the English language.
First-rate; excellent: a capital idea.
A town or city that is the official seat of government in a political entity, such as a state or nation.
A city that is the center of a specific activity or industry: the financial capital of the world.
Wealth in the form of money or property, used or accumulated in a business by a person, partnership, or corporation.
A building or complex of buildings in which a state legislature meets.
The building in Washington, D.C., where the Congress of the United States meets. See Usage Note at capital1.
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").