Okay, let's just rip this bandaid off right away. Not these dragons:
Mostly because those dragons, despite the recent publication of their phylogeny, are mythical. But also because Operational Health & Safety would never approve the risk assessment. The dragons I work with are much more adorable:
The dragons I study are part of the mostly Australo-Papuan group of lizards which are referred to as "dragons". The scientific name for this group is Amphibolurinae. To anyone outside of Australia, the most familiar members of this group are probably the bearded & Chinese water dragons, both of which are commonly sold in pet shops across the Americas, Europe, and Asia. In Australia, dragons are well known because they're diurnal and like to bask in the sun from conspicuous locations such as rock piles, bushes, and trees.
How can you tell a dragon from any other lizard? Well, you probably can't. Neither could I. I cannot think of a single morphological character that would allow me to look at a lizard and identify it as a dragon (i.e. a member of the Amphibolurinae), nor can I find any in the literature. Genetically, however, they are distinctly their own group. Amphibolurine dragons are part of a larger group of lizards called agamids, which are identifiable from skeletal characteristics, but still there are no external morphological features that would allow you to look at an agamid and identify it as such. Here's a non-dragon agamid:
Some agamids that are not amphibolurines may also be called "dragons", notably the flying dragons of the genus Draco and the mountain horned dragons of Acanthosaura. These are members of another agamid group, the Draconinae. Since, as any HP fan can tell you, "draco" means "dragon" in Latin, that's fair enough. It's interesting, though, that every species of amphibolurine carries the name dragon (with one notable exception), however the name seems to be only haphazardly applied to a few species within Draconinae, a group literally called "the dragons".
There is another lizard out there referred to as a dragon:
Komodo dragons are not closely related to the agamid dragons. They are members of the Varanidae, which are known as goannas (to Australians) or monitor lizards (to the rest of the world) and they are closely related to gila monsters and snakes. Agamids are off quite a different branch of the lizard evolutionary tree. Their closest living relatives are the chameleons and iguanids. Here's a sample chameleon, the closest living relative of the agamids:
There is one last dragon I can think of. I would love more than anything to be able to study this dragon:
And by "study" I mean "be best friends with".