Metonymy – is a RELATED object Synecdoche is a PART of the SAME object

My mommy is related to me (metonymy), but my sin is a part of me (synecdoche).

My neck is a part of me, but Tony and I are only related.

Synecdoche: using a part of something to represent a whole

Example: All hands on deck.

Metonymy: refer to something closely related to the object, instead of saying the actual subject

Example: The White House answered its critics.

Examples of Metonymy

This statement includes two examples of metonymy:

“The pen is mightier than the sword.” In the oft-quoted phrase, "the pen" refers to the the written word, which, according to the statement, is a more effective and powerful instrument of change than "the sword," which represents military or physical force. When students say they study “Shakespeare,” they generally do not refer to a study of the man himself, but of his literary works. When we use the term “the press,” we are referring to journalists, not to the actual printing press that produces their work. Part of a Whole All poodles are dogs, but not all dogs are poodles. All synecdoche is metonymy, but not vice versa. Synecdoche is a special form of metonymy in which the object or idea used to describe something larger is actually a part or a component of the larger idea. This device may also be used when a smaller group is used to reference a larger group with which it is a part. “Hollywood” refers to the entire American movie making industry, not the suburb that was named “Hollywood.”

Examples of Synecdoche:

“I got a new set of wheels” usually means, “I bought a new car,” of which wheels are a part.

“Boots” can refer to “soldiers,” and “sails” to an entire ship. A specific brand of a product often comes to be used to describe a larger category.

“Coke” is sometimes used to describe all colas,

“Band-Aid” to describe any small adhesive bandage, and "Kleenex” to refer to any facial tissue. In "The Face that Launched a Thousand Ships," poet Christopher Marlowe writes, "Was this the face that launched a thousand ships, / And burnt the topless towers of Ilium?" The entire Greek military is represented by a part, "a thousand ships," while "the towers" represent the entire city and culture of Troy, and Helen's "face" is a part of her body that refers to her physical beauty as a whole.

References:

http://slideplayer.com/slide/8495783/

http://classroom.synonym.com/examples-metonymy-synecdoche-22055.html