Draconian describes something as very strict or harsh. It comes from the Athenian lawmaker Draco, whose laws were extreme. For example, theft carried the death penalty. While it was previously capitalized, because Draco is a name, most do not capitalize it today.
It should be noted that draco is also a Latin word meaning dragon or snake. Common confusion arises with the word draconic, which originally meant pertaining to dragons, but was commandeered after Draco came onto the Athens political field. Therefore, it carries both meanings and one must use context to determine the definition.
Dragonian, on the other hand, derives from the word dragon not draco and most definitely pertains to dragons.
Below is the ngram for draconian, which has been on a steady rise for the past fifty years.