This question is actually dependant on location. Terrapins are turtles, but in several countries the term terrapin is used interchangeably with the term turtle for various species. There are several species whose common name is specifically Terrapin such as the Painted River Terrapin from Southeast Asia or the Diamondback Terrapin from the United States eastern seaboard. In the United States the term Terrapin is used for the Diamondback terrapin to separate this species as the only species to live exclusively in brackish water. The term Terrapin actually derives from an indian word meaning "little turtle".
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