Mahayana-specific definition of "a buddha"? We all know the Pali Canon's definition of "The Buddha". The Buddha is one who discovers The Dhamma all by himself without external help, therefore by definition there may be only one Buddha until the teaching is completely forgotten and thus can be re-discovered.

In Mahayana, the situation seems to be different. When Mahayana texts speak about "a buddha" they seem to put a different meaning into this word. In Mahayana, a buddha is someone -- or indeed anyone -- who has attained anuttara-samyak-sambodhi - the Complete and Perfect Enlightenment.

At the same time, it does look like in many Mahayana contexts, the term "buddha" may be used rather too liberally. I'm not talking about the precepts, or the laity (which is what I am, at best). We all know that the Dalai Lama is said to be a tulku of Avalokiteśvara, and is presumably a Bodhisattva on the 10th -- correct me if I'm wrong -- Bhumi, and very, very close to enlightenment. I don't know of any similar claims in Tantric traditions outside Tibet. But the Tantric teachings propagated to Tibet via certain Indian masters, ones that East Asian Buddhism claim to share lineage with. Similarly, I know that some contemporary Korean Son monks have claimed to be Buddhas. 


  Seongcheol was widely recognized in Korea as having been a living
  Buddha, due to his extremely ascetic lifestyle, the duration and
  manner of his meditation training, his central role in reforming
  Korean Buddhism in the post-World War II era, and the quality of his
  oral and written teachings.


I do not believe this is a complete anomaly. Huineng (the 6th Patriarch in China), as well as writing a "Sutra", was said to be on the 10th Bhumi (at least -- though I have read some Western commentators say this is just impossible with standard definitions of the Bhumis) by his disciple Shen-hui, whom I believe all Soto and Rinzai Buddhists, in deed all Buddhists that base their teachings primarily on Huineng, claim is in their lineage.

I am aware that some Tantric traditions do teach "Buddhahood in this very body".

But equally, there is a tradition of great humility in Mahayana Buddhism. The great Tientai (which mutated into Japanese Tendai) master Zhiyi claimed not even to have the appearance or semblance of enlightenment to his practices. Zongmi, who I believe may still be important in Korea, was of a similar, Hua-Yen and Ch'an, mind.

So, where is "the bar"? E.g., are all genuine masters Buddhas -- or near as darn it. That may seem crazy. But are all Buddhas, according to the Mahayana, reborn from the Tusita heaven?
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.