The words vail, vale, veil sound the same but have different meanings and spellings. Why do vail, vale, veil sound the same even though they are completely different words?
The answer is simple: vail, vale, veil are homophones of the English language.
To lower (a banner, for example).
To doff (one's hat) as a token of respect or submission.
To descend; lower.
To doff one's hat.
A valley, often coursed by a stream; a dale.
Used to express leave-taking or farewell.
A length of cloth worn by women over the head, shoulders, and often the face.
A length of netting attached to a woman's hat or habit, worn for decoration or to protect the head and face.
The part of a nun's headdress that frames the face and falls over the shoulders.
The life or vows of a nun.
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").