Concerning the word "cliché" it is used in French as follows:
For what is often called a "lead": Imprint of a die during the manufacturing process. It is often taken on pewter or lead.
For "electrotype": A reproduction of a coin or medal made by an electroplating process.
(From my The Canadian Dictionary of Numismatics | Le dictionnaire canadien de numismatique)
"Cliché" in non-numismatic French means "snapshot" (as in photo), so its numismatic use is very logical since it is a snapshot of a die. Can't see how it can be related to the sound of a press!
Another use for the term cliché, also dealing with thin metallic objects, is in stamp printing. Back in the days before siderography, and when stamps were printed using letterpress technology, sheets of stamps were printed from frames of individual stamp clichés locked into place. One of the most famous stamp errors, the Swedish 3 skilling banco in yellow, was probably created when a 3 skilling banco cliché was mistakenly inserted into a plate of 8 skilling banco clichés, and the resulting stamp was printed in the yellow color of the 8 (the 3 was supposed to be blue-green).
Clichés were made by stereotyping (casting from a master image), and another definition of stereotyper is a machine that creates embossed plates - thus the embossing that Dick Hanscom's original query described.
The use of the word cliché there has nothing to do with its use by a medal maker. And I have to take exception to Dick Johnson's (perhaps tongue in cheek) statement that "The term cliché comes from the sound the press made when striking these ...." The term cliché comes from the French for stereotype (as a verb) - and is carried into English as yet another (but not unrelated) definition of stereotype - a hackneyed phrase, a repeated reference - because, in its original use, clichés were all alike.