Here's a blurb I wrote for another forum about a year ago, with some additions:
So what -is- the difference between a tortoise and a turtle anyway? Well, to be technical, tortoises belong to their own group within the order of Testudines (turtles) called Testudinidae. To get less scientific, the difference is largely in how and where they live and how they have adapted to that environment.
Tortoises are strictly terrestrial, and in general have adapted a larger, more domed shell. Their limbs are specialized for digging and pushing.
Sulcata tortoise front leg. Very strong and well armored.
Sulcata tortoise rear leg - notice the almost elephant-style foot.
The distinction between water turtles and box turtles is a little more confusing. Box turtles are members of the group Emydidae, which also includes most fresh water turtles like sliders, cooters, painteds, as well as terrapins. Box turtles are terrestrial and have a domed shell. Their front feet more adapted to digging, though sometimes found near water, they don't generally spend time in water - though they can swim.
Box turtle, notice the long claws and strong front legs.
Aquatic (or mostly aquatic in the majority of cases) turtles have webbed feet - and while they can have long claws sometimes and can walk just fine on land are obviously more suited to swimming. Their shells tend to be flatter than their terrestrial cousins.
The front foot of a female red-eared slider. Note the webbing between the toes.
The only real distinction that makes terrapins different is that they live in brackish (somewhat salty) water. Their body structure is very similar to other aquatic/semi-aquatic members of the group Emydidae. They tend to be strikingly marked and are on the brink of extinction because of their desire in the food market. Apparently they taste good.