The earliest traceable specimens of this class are certain counterstruck imitation silver drachms of Phraates IV,... (Source)
What does "counterstruck" mean?
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First of all, coin striking is the process of taking a "blank" coin and stamping it with a die so that it now has a picture or other marking on each side.
Secondly, the author(s) of the paper appear to use "counterstruck" and "countermarked" interchangeably, as indicated in this quote from page 27:
The strikers of the imitation Hermaios coinage were probably also responsible for a group of Arsakid drachms which were countermarked, or imitated and then countermarked (MA 1-5). It has been demonstrated that the nature of these counterstrikings was benign, ...
Finally, a countermark is:
an additional mark or symbol punched into [a coin] at some point during its career as a circulating coin.
If a coin is counterstruck (or overstruck), an existing coin is treated like a blank so that the old image is obliterated by the new image.
I found the following definition in a forum for coin collectors, unfortunately without the original source:
OVERSTRIKE (COUNTERSTRIKE)- coin struck over an older and usually worn coin used as a planchet [eg, 1804 Bank of England 5-shilling piece struck on a Spanish dollar]