The words waiver, waver sound the same but have different meanings and spellings. Why do waiver, waver sound the same even though they are completely different words?
The answer is simple: waiver, waver are homophones of the English language.
Intentional relinquishment of a right, claim, or privilege.
The document that evidences such relinquishment.
A dispensation, as from a rule or penalty.
Permission for a professional athletic club to assign a player to the minor leagues or release a player from the club, granted only after all other clubs have been given the opportunity to claim the player and have not done so.
To move unsteadily back and forth. See Synonyms at swing.
To exhibit irresolution or indecision; vacillate: wavered over buying a house. See Synonyms at hesitate.
To become unsteady or unsure; falter: His resolve began to waver.
To tremble or quaver in sound, as of the voice or a musical note.
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").