The figurative meaning of a word refers to the extra meaning that is different from its literal meaning and should be taken at face value.
This refers to the implied meaning of a word that is different from its denotative meaning and can be determined through the aid of context clues.
Hence, we can see that the two are similar, but the main difference between them is that figurative meaning can be either metaphoric, hyperbolic, onomatopoeic, etc, but the connotative meaning of a word can be found in the dictionary and is an alternative meaning.
Read more about connotative meanings here:
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