Dragon taxonomy is a path best not thread, I fear.
All attempts at establishing a solid taxonomy has failed. Grand Sage Wickerstaff (the elder)'s work 'The Sage's Taxonomy of Dragons, Drakes and Dregs' is an oft referanced tome on the subject, and while it is a usefull starting point, as you dive into it, you'll find a rather startling number of contradictions and missclasifications.
Once I learned that the North Sea Lesser Wyrm, classified in the Sage's Taxonomy as a member of the legg-less sub-clade of the north-western wyvern grouping, was, in truth, a monotereme, I decided to cease my study of the feild.
The natural world oft eludes our desires to classify it, but the addition of magic to the mix has not simplified the matter of dragon taxonomy, to say the least.
My best advice is to use the common descriptors and common names for dragons of all variation, and give up on any taxominal rigidity.
A North Sea Lesser Wyrm is a wyrm in the same way a tomato is a vegetable and a strawberry is a berry. Unless you have a deep fascination for the finer details of taxonomy, do not delve any deeper into it than that.
To answer your original questions, pardon my slight deviation, there are dragons in mamalia, reptilia, arthropoda, and other groups, as well as unique groups with nothing but magical creatures.
There are dragons smarter than any living mortal, dragons as unthinking as coral, and the full spectrum between them.
The firebreathing kinds use all manner of means to do so, direct magic, chemistry, alchemy, and other means. Some have special organs, others inate magical abilites, other re-use other organs. My favorite are the 'storage' dragons, in particular the the Nyiragongo Minutre Drake is fascinating. It's a small drake, about the size of a rat, and it does not so much breathe fire, as regurgitate magma. It's an amazingly efficent hunter, bringing down prey far far larger than it, since, well, few things can survive a glob of magma to the face.
If you are further interested in the taxonomy of dragons, I recommend applying to view the taxonomy section of the Library of Alexandira over in the fire-realm. They've been quite dilligent in keeping their records on dragons up to date, as far as I can tell.