ringing / wringing 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. 👇
ringing: (noun) the giving of a ring as a token of engagement.
wringing: (verb) twist and compress, as if in pain or anguish. (verb) twist, squeeze, or compress in order to extract liquid.
ringing: r·IH·ng·ih·ng
wringing: r·IH·ng·ih·ng
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)