The words rooting, routing sound the same but have different meanings and spellings. Why do rooting, routing sound the same even though they are completely different words?
The answer is simple: rooting, routing are homophones of the English language.
Originally, a system of roots; a secure attachment (in something); a firm grounding.
The process of forming roots.
A method of creating a new plant by getting part of an existing plant to form roots.
Present participle of root.
a method of finding paths from origins to destinations in a network such as the Internet, along which information can be passed
cutting a channel in a material such as wood using a router
Present participle of route.
Present participle of rout.
Definitions 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.