The words greave, grieve sound the same but have different meanings and spellings. Why do greave, grieve sound the same even though they are completely different words?
The answer is simple: greave, grieve are homophones of the English language.
Leg armor worn below the knee. Often used in the plural.
To cause to be sorrowful; distress: It grieves me to see you in such pain.
To mourn or sorrow for: We grieved the death of our pastor.
Usage Problem To file an official or formal grievance on account of (an actual or perceived injustice).
Archaic To hurt or harm.
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.