Mahayana-specific definition of "a buddha"?
Traditionally in Mahayana (esp. Zen and Tibetan) the student considers the teacher to be a perfect expression of the Eternal Buddha-Nature, "eternal buddha" in short. While the teacher himself traditionally downplays his realizations, sometimes as far as "These are the words of my perfect teacher and I'm just a dumb guy" etc.

The first point goes in line with the idea that all Teaching about ultimate Reality is by definition an expression of said Reality. Therefore anything or anyone that teaches Sat-Dharma is a continuation of Dharmakaya of Buddha - a continuation of Buddha in short - hence "the eternal Buddha":


  I, Kuntuzangpo, am the original Buddha of all, and through this prayer
  of mine, may all you beings who wander in the three realms of samsara
  realize this self-arising awareness, and may your great wisdom spontaneously
  increase.
  
  My emanations will continuously manifest in billions of unimaginable
  ways, appearing in forms to help you beings who can be trained.


The second point goes in line with the Mahayana realization that Enlightenment is attainment of no-attainment, and so does not represent anything special to be proud of:


  Subhuti again asked, “Blessed lord, is it true that when you attained Complete Perfect Enlightenment, nothing have been attained?”
  
  The Buddha replied:
  
  This is right, this is right, Subhuti. As to Complete and Perfect Enlightenment, there is absolutely nothing that I attained, and this is why it's called Complete and Perfect Enlightenment.