The words ad, add sound the same but have different meanings and spellings. Why do ad, add sound the same even though they are completely different words?
The answer is simple: ad, add are homophones of the English language.
An advertisement.
An advantage in tennis.
To combine (a column of figures, for example) to form a sum.
To join or unite so as to increase in size, quantity, quality, or scope: added 12 inches to the deck; flowers that added beauty to the dinner table.
To say or write further.
To find a sum in arithmetic.
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").