The words aerial, ariel sound the same but have different meanings and spellings. Why do aerial, ariel sound the same even though they are completely different words?
The answer is simple: aerial, ariel are homophones of the English language.
Of, in, or caused by the air.
Existing or living in the air.
Reaching high into the air; lofty.
Suggestive of air, as in lightness; airy.
Common misspelling of aerial.
type of mountain gazelle, native to Arabia
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").