The words tael, tail, tale sound the same but have different meanings and spellings. Why do tael, tail, tale sound the same even though they are completely different words?
The answer is simple: tael, tail, tale are homophones of the English language.
Any of various units of weight used in eastern Asia, roughly equivalent to 38 grams (1 1/3 ounces).
A monetary unit formerly used in China, equivalent in value to this weight of standard silver.
The posterior part of an animal, especially when elongated and extending beyond the trunk or main part of the body.
The bottom, rear, or hindmost part: the tail of a shirt.
The rear end of a wagon or other vehicle.
The rear portion of the fuselage of an aircraft.
Archaic A tally or reckoning; a total.
A recital of events or happenings; a report or revelation: told us a long tale of woe.
A malicious story, piece of gossip, or petty complaint.
A deliberate lie; a falsehood.
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").