The link between two things in a metonymy is associative. For example, "The White House has recently come out and said..." The White House stands for the office of the president based on the conventional association between these two things.
The link between two things in a metaphor is based on a perceived similarity between two unlike things. For example, "Love is heroin." In this case, love is compared to heroin not because heroin is associated with drug addicts being in love, but because love itself is like an addictive substance in its very nature.
But this difference between metonymy and metaphor raises an interesting question about clichéd metaphors. Basically, it stands to reason that a metaphor like "love is a rose" is not a metaphor at all, but a metonymy. This is because over time, the phrase has become so overused that people have forgotten whatever first inspired the comparison, and now know only that love and roses are connected on the basis of conventional association.
The point of all of this is to say that metaphor is a living, breathing thing. A metaphor that becomes a cliché actually demonstrates the organic principle of language. If the link between love and roses shifts from perceived resemblance to conventional association over time, then it stands to reason that any frequently used metaphor will degenerate into a metonymy over time. In their essence, all clichés are metonymies. That's why writers must endlessly come up with new, fresh metaphors. Their poetic effect has an expiration date, and metonymy is what they turn into when their once-nourishing milk has curdled.
Metonymy is rot and death.
Metaphor is freshness and life.
For a more in-depth look at my theory of "The Genealogy of Metaphor & Metonymy," see pages 31 to 50 of my doctoral dissertation, titled "Feeling Better: The Therapeutic Drug in Modernism": http://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1374&context=etd