The words heigh, hi, hie, high sound the same but have different meanings and spellings. Why do heigh, hi, hie, high sound the same even though they are completely different words?
The answer is simple: heigh, hi, hie, high are homophones of the English language.
An exclamation designed to call attention, give encouragement, etc.
Informal Used to express greeting. See Regional Note at hey.
To go quickly; hasten.
Having a relatively great elevation; extending far upward: a high mountain; a high tower.
Extending a specified distance upward: a cabinet ten feet high.
Far or farther from a reference point: was too high in the offensive zone to take a shot.
Being at or near the peak or culminating stage: the high tourist season; high summer.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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.