Diamondback terrapin

or just "terrapin"

Malaclemys terrapin,

a turtle of the Emydidae family, native to the US

European pond terrapin

or European pond turtle

Emys orbicularis,

a turtle in the family Emydidae found in West Asia and parts of North Africa

Mexican spotted terrapin 

or Mexican spotted wood turtle

Rhinoclemmys rubida,

a species of turtle in the family Geoemydidae, endemic to Mexico

Painted terrapin Batagur borneoensis,

a turtle in the Geoemydidae family native to Brunei, Indonesia, Malaysia, and Thailand

Northern river terrapin Batagur baska,

a critically endangered turtle in the Geoemydidae family native to Cambodia

Southern river terrapin Batagur affinis,

a turtle in the Geoemydidae family native to Cambodia

Smiling terrapin 

or Black marsh turtle

Siebenrockiella crassicollis,

a turtle in the Geoemydidae family native to Southeast Asia

Seychelles black terrapin Pelusios seychellensis,

an extinct species of turtle in the Pelomedusidae family that was endemic to Seychelles

Serrated hinged terrapin Pelusios sinuatus,

a species of turtle in the Pelomedusidae family found in southern Africa

Striped-neck terrapin

or Caspian turtle

Mauremys caspica,

a turtle in the family Geoemydidae (Bataguridae), native to the eastern Mediterranean region

Bengal eyed terrapin, Burmese eyed turtle or Burmese peacock turtle Morenia ocellata,

a turtle in the family Geoemydidae found in Burma and possibly Yunnan, China

Indian pond terrapin

or Indian black turtle

Melanochelys trijuga,

a turtle in the family Geoemydidae found in South Asia