The words morning, mourning sound the same but have different meanings and spellings. Why do morning, mourning sound the same even though they are completely different words?
The answer is simple: morning, mourning are homophones of the English language.
The first or early part of the day, lasting from midnight to noon or from sunrise to noon.
The dawn.
The first or early part; the beginning: the morning of a new nation.
The actions or expressions of one who has suffered a bereavement.
Conventional outward signs of grief for the dead, such as a black armband or black clothes.
The period during which a death is mourned.
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").