Here are the differences between the two words:
The term "meronymy" is used to describe the part-whole relationship between items, for example: kitchen, bathroom and den are meronyms of house. A meronymy is a classification system similar to a taxonomy.
A metonymy, on the other hand, is more of a literary device than a classification system. The term "metonymy" is used for a identifying a referent by a word that is associated with it, for example: The White House is a metonym for the President and the Press is a metonym for news media (The Press sure ran with that story).
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