The term Pureblood is most frequently used on demons that aren't mixed with any other species within the last five or six generations - although where the line goes between demons and other human-like species is questionable at best. Technically the term would apply on any specie but in this universe it's normally reserved exclusively for demons and are used more as a social standard: there are demons, and there are pureblood demons.
A scientific test of genetics would probably reveal that neither is even remotely as pure as other accepted species. This is because demon genes aren't meant to be pure. Their genetic design is made so that they technically should be able to breed with any specie that is physically compatible with them. However, the word holds a lot of claim and sounds rather noble - especially to Ashigori traditionalists.
The question becomes solvable through the demon philosophy on Truth and Reality. Reality is what you see - pure facts. Truth is what it is - what is believed and lived after. That some demons are more pure than others is claimed to be true by so many demons that it is True. This Truth isn't argued against because it is backed up by a Reality where purebloods hold a significant power backed up by myth.