The words hide, hied sound the same but have different meanings and spellings. Why do hide, hied sound the same even though they are completely different words?
The answer is simple: hide, hied are homophones of the English language.
To put or keep out of sight; secrete.
To prevent the disclosure or recognition of; conceal: tried to hide the facts.
To cut off from sight; cover up: Clouds hid the stars.
To avert (one's gaze), especially in shame or grief.
To go quickly; hasten.
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").