The words rigger, rigor sound the same but have different meanings and spellings. Why do rigger, rigor sound the same even though they are completely different words?
The answer is simple: rigger, rigor are homophones of the English language.
One that rigs: oil and gas riggers.
Nautical A ship with a specific kind of rigging.
Strictness or severity, as in temperament, action, or judgment.
A harsh or trying circumstance; hardship. See Synonyms at difficulty.
A harsh or cruel act.
Medicine Shivering or trembling, as caused by a chill.
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").