The words board, bored sound the same but have different meanings and spellings. Why do board, bored sound the same even though they are completely different words?
The answer is simple: board, bored are homophones of the English language.
To enter or go aboard (a vehicle or ship).
on board Aboard.
A long flat slab of sawed lumber; a plank.
A flat piece of wood or similarly rigid material adapted for a special use.
Simple past tense and past participle of bore. A bored woman selling souvenirs in Moscow.
suffering from boredom
uninterested, without attention
perforated by a hole or holes (through bioerosion or other)
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").