auger / augur 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. 👇
auger: (noun) hand tool for boring holes.
augur: (noun) (ancient Rome) a religious official who interpreted omens to guide public policy. (verb) predict from an omen.
auger: AO·g·er
augur: AO·g·er
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)