The words installation, instillation sound the same but have different meanings and spellings. Why do installation, instillation sound the same even though they are completely different words?
The answer is simple: installation, instillation are homophones of the English language.
The act of installing.
The state of being installed. Also called installment2.
A system of machinery or other apparatus set up for use.
A permanent military base.
The act of instilling; also, that which is instilled.
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").