rout / route are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
rout: (noun) an overwhelming defeat. (verb) cause to flee. (verb) dig with the snout. (verb) make a groove in.
route: (verb) send documents or materials to appropriate destinations. (verb) send via a specific route. (verb) divert in a specified direction.
rout: r·AW·t
route: r·UW·t
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)