The words grill, grille sound the same but have different meanings and spellings. Why do grill, grille sound the same even though they are completely different words?
The answer is simple: grill, grille are homophones of the English language.
To broil on a gridiron.
To torture or afflict as if by broiling.
Informal To question relentlessly; cross-examine.
To mark or emboss with a gridiron.
A grating of metal, wood, or another material used as a screen, divider, barrier, or decorative element, as in a window or on the front end of an automotive vehicle.
An opening covered with a grating.
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").