The words equater, equator sound the same but have different meanings and spellings. Why do equater, equator sound the same even though they are completely different words?
The answer is simple: equater, equator are homophones of the English language.
The imaginary great circle around the earth's surface, equidistant from the poles and perpendicular to the earth's axis of rotation. It divides the earth into the Northern Hemisphere and the Southern Hemisphere.
A similar great circle drawn on the surface of a celestial body at right angles to the axis of rotation.
The celestial equator.
A circle that divides a sphere or other surface into congruent parts.
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").