coffer / cougher 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. 👇
coffer: (noun) an ornamental sunken panel in a ceiling or dome. (noun) a chest especially for storing valuables.
cougher: NA
coffer: k·AO·f·er
cougher: NA
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)