Different cultures have indeed given different names to supernatural beings, but there is a surprising consistency in the basic self-regarding moral laws of nearly all cultures, however far separated.
Thus you have Confucius stating that the highest principle was to be other-regarding, to not do to another what one would not want done to one's self.
And you have the prince in the Bhagavad Gita breaking down suddenly in battle when he has an epiphany and realizes that the men he is fighting are really akin to him, like cousins, so how can he kill them?
The golden rule of the Christians and of the Jewish Hillel are famous.
The 27 commandments of the Chippewa were very similar in moral tone.
Now, different rules always applies when dealing with other enemies outside the group, but the "group" has almost always been loosely defined enough to let others in by some process of conversion.
So, although men might call angels or demons by different names all the world around, yet there is a remarkable parallellism across cultures and times concerning the moral rules for the treatment of one's own, and in referring to various gods or divine inspiration for these good principles.
This is what allows various religions of the world, although quite hostile to each other in other ways, to recognize that the same god or gods have roamed the earth under many names, also the same demons, exhorting men to do or not to do the same things all the world around.
There is a reason why the conversion of Ireland and the North American woodland Indians was practically a walkover: the Irish already had the moral code and the inclination towards monotheism or a great spirit. The Christians merely gave those spirits names. There already was substantial "Christian" morality among the Irish and the Chippewa before the Catholic missionaries showed up.
The Christian improvement on these native revelations was to assign a name to God, and to suggest that the rules as applied WITHIN the group should also be applied to those OUTSIDE of the group. The Hindus in particular had the same inspiration.
To me (and to Hindus, Muslims and Chippewa animists), this shows One God at work, giving the same inspirations to each different tribe and group of people, distilled through the familiar cultural prisms of these people. The banal uniformity of evil and desire for it is also everywhere visible. This too is revelatory of something.
"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.