"This is a perplexing position you've taken. It leads me to wonder what criteria you use to differentiate concepts from one another, if not by name, time of origin, location of origin, appearance, disposition, or history."
The Christian criteria are "Divine Revelation". It does require an aspect of proof. For example a madman raving that that he has seen the face of God and this is what he told me to tell you guys is not sufficient. It requires a bit more than one person saying "this is true".
Since events in the ancient pass are so often dismissed just because they did not happen now is a common reaction allow me to give you a good and fairly modern event that the Roman Catholic Church has ruled as valid? It will give you an example of the sort of Criteria you are asking about. (I am assuming you are sincere in this)
In 1917 in Portugal (Fatima to be specific) there were 3 children (the oldest about the age of 10) started seeing the Blessed Mother. Crowd started to follow the children to the site of these visions on the days they were expected. Each time the crowds got larger and many of the crowd saw unusual things. It ended with a very impressive vision seen by the 70,000 observes involving the dancing of the sun. It had rained all night and into the morning and everyone there was sopping wet when it all started. In a few moments the ground was made dry and the people's wet clothing was dried. This one item alone is not explainable in science and everyone surviving the process to dry everything out in the short time that it occurred. (A process to do this would result in the death of those present if you are only willing to see such an event as a natural/worldly as explained by science)
This was witnessed my faithful Catholics of course but also a large number of disbelievers. Portugal at the time was being ruled by an anti-Catholic and anti-Christian government. Many there were atheist and other assorted types. The children had many predictions on world events that have come true.
There are a few things to know about the whole thing.
1. The children did not have the education or worldly knowledge to make an educated guess about the future.
2. The children never said a single thing that was against Catholic Theology which may have happened if they were faking.
3. The miracles that occurred were witness by many and many were hostile to the Catholic faith.
4. Science can not explain the entire event.
5. The event has been examined by the appropriate religious authorities who also sought out advice on the matter from science and those who where there and not just Catholics.
This is much more on this event should you wish to see it. There are other examples but I can think of no other religion that looks at such events with real hesitations and has to be convinced through real scholarship even using science to evaluate it.
The criteria are stricter in this one case alone than what often passes for criteria in the modern scientific community today. If you are a regular reader of FR you most likely can think of a few examples of this sort of thing without my help.
For more on the events at Fatima you can find many websites on the subject. Here are just a few:
http://www.angelfire.com/id/bvm/OurLadyofFatima.htm
http://www.fatima.org/
http://www.santuario-fatima.pt/portal/index.php?id=1000
I hope this example answers your question.