Turtles sort of cheat their way into having an "exoskeleton", but it's not a true one. The carapace is comprised of modified vertebrae (neural bones) and ribs (costal and peripheral bones). The plastron was once thought to be a modified sternum, but it actually seems to be composed of the clavicles and gastralia, a structure found only in reptiles.

Turtles have all the same bones as other vertebrates, and their internal organs are still housed within a body cavity protected by bone. They've just gone a little overboard with the level of protection. One can jokingly refer to their shell as an exoskeleton, but it is in reality a highly modified endoskeleton.

Turtle morphology is endlessly fascinating and has baffled researchers for decades, both in terms of how they relate to one another and how they relate to other reptiles. We're finall starting to parse them out based on genetics, but even still it's tricky and involved. I don't deal with genetics though, I just put my faith in the geneticists.