There seem to be two different things to address here.
1) There is a distinction between creatures that either result from Dark Magic (werewolf) or acts in a Dark way (hinkypunk), versus creatures that just are or have little to no magical relevance to be defended against.
Hinkypunks lure travelers to with a lantern to deceive them. Lycanthropy is the result of a magical illness, spread through saliva and blood. These make them topics to discuss in Defense against the Dark Arts.
Creatures such as Thestrals or Hippogriffs on the other hand don't exactly go out of their way to act in a malicious or unnatural way. It can be unnerving to think of a creature that can only be seen by the dead etc., but at the core they're just creatures. There's no specific magical defense to be studied.
2) The classes have different purposes. One is obviously to take Care of a creature, deal with things like interacting with it, bonding with it, breeding it, etc. The other is to Defend against dark magic, and creatures that involve dark magic, or behave in a dark way. "Danger" is not the exclusive province of either.
Now, this won't exactly be in the lessons because they aren't "official" creatures and wouldn't have had the change to make it into a syllabus, and only Hagrid might have seen them as creatures worth caring for, but Blast-Ended Skrewts are a pretty good candidate for being in both classes.
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2 years ago
Lupin, in particular, taught his DADA students (or his third year ones anyway) almost entirely about Dark magical creatures (red kaps, hinkypunks, werewolves, etc). I find it interesting that there are also dangerous creatures in many of the Care of Magical Creatures lessons. Is there any evidence of a divide that says that werewolves and hinkypunks are Dark Magic, whereas hippogriffs are potentially dangerous magical creatures like a magical tiger or leopard, but not Dark? Obviously the focus of the lesson is defence vs care, but is there a difference in the classification of the creatures? Another question to show what I'm thinking (but not to include multiple quetions) is do any of the creatures overlap into both subjects?