1) There is no set definitions. Its true. Take terrapin.
Oxford's Compact Dictionary says: • noun a small freshwater turtle.
Not very specific is it? Also many herpetologists and some herp texts will say that terrapins live in brackish water.
Oxford says noun 1 a marine or freshwater reptile with a bony or leathery shell and flippers or webbed toes.
Other dictionaries give other definitions like:
Any of various aquatic or terrestrial reptiles of the order Testudines (or Chelonia), having horny toothless jaws and a bony or leathery shell into which the head, limbs, and tail can be withdrawn in most species.
Ok, one says they are aquatic one says they are either aquatic or terrestrial.
The only one anyone seems to have any form of agreement on is tortoise.
: any of a family (Testudinidae) of terrestrial turtles; broadly : turtle
:noun a slow-moving land reptile with a scaly or leathery domed shell into which it can retract its head and legs.
Wait, that is not really specific. Well most agree that tortoises are terrestrial.
The fact is that nothing is really settled and there are regional uses of the words.To make things even more confusing, the scientifically accepted common name of the eastern box turtle is eastern box turtle and the scientific taxonomic name is Terapene carolina. So here is an example of an animal that is both a terrapin and a turtle! What is more is that it is terrestrial!
2) Take a definition and run with it. That is the best thing you can do. Most of the herpetologists I deal with use the following set of definitions, and I use this set too because it gives us a standard that we can use.
Turtle: any testudine, a broad term roughly synonomous with Testudines and including aquatic and terrestrial species.
Tortoise: any terrestrial testudine (turtle) that generally has elephantine appendages and a high domed shell (though the shell has its exceptions). The most commonly accepted genera for tortoise standards are Geochelone and Testudo.
Terrapin: any turtle on the table or in the kitchen. The term terrapin came from the Algonquin Indian language and meant edible turtle. Thus, it is a culinary term not really a scientific term, and should remain so. Only when it is part of the accepted name should it be used such as Diamondback Terrapin, but it should not be used to refer to a group of animals as a way of classification, unless you are a chef.