The words conker, conquer sound the same but have different meanings and spellings. Why do conker, conquer sound the same even though they are completely different words?
The answer is simple: conker, conquer are homophones of the English language.
A horse-chestnut used in the game of conkers.
To defeat or subdue by force, especially by force of arms.
To gain or secure control of by or as if by force of arms: scientists battling to conquer disease; a singer who conquered the operatic world.
To overcome or surmount by physical, mental, or moral force: I finally conquered my fear of heights. See Synonyms at defeat.
To be victorious; win.
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.
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").