rhyme / rime 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. 👇
rhyme: (noun) correspondence in the sounds of two or more lines (especially final sounds). (verb) compose rhymes. (verb) be similar in sound, especially with respect to the last syllable.
rime: NA
rhyme: r·AY·m
rime: NA
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)