Are terrapins and turtles the same?
Yes and no, you see turtles are an entire family of animals (snapping turtles, sea turtles tortoises, and terrapins) Terrapins are pond turtles as in they live in ponds and lakes, unlike tortoises or sea turtles.
You brought a turtle yellow bellied is it the same as a yellow bellied terrapin if not how can you tell the difference?
Both names refer to the same animal. In America terrapins, tortoises and turtles are all referred to as turtles. This has caused some confusion in the hobby and some pet/reptile shops here in the UK also call terrapins turtles. The peninsular cooter (also a terrapin) looks almost identical to the yellow bellied terrapin. Hope this helps.