What differentiates the Valar from the Maiar?
 

What differentiates the Valar from the Maiar? They are both Ainur, correct?

Also, were the Maiar as old as the Valar--did all the Ainur come into being at the same time, in the Beginning? More to the point, would the spirit later known in Arda as Gandalf, have taken part in the Song? Would Gandalf have been there in the Beginning with the rest of the Ainur?

In a nutshell, the Vala are fewer and more powerful than the Maia.

Yes. In short, the difference is purely nominal, I would say - the Valar are simply more powerful. It says that Valar are "the chief among the Ainur", but in fact, Valar and Maiar are rather, hmm, misleading division, because technically, they are all the same order of beings. The difference between Valar and Maiar is more akin to difference between, say, kings and common folk than between Elves and Dwarves, for example. Merely a question of power and status.

Definitely equally old; also, if for nothing else, because there was no "time" before that.

The Valaquenta notes that Melkor "was coeval with Manwe". The word "coeval" means of the same age indicating that Manwe & Melkor were created at the same time.

It's not absolute, but this suggests that the Ainur were not all created at the same time (else, what is the point of highlighting that two in particular WERE?). The Ainulindale only says that Eru made the Ainur "before aught else was made" - not that he made them all in the same instant.

While many Ainu entered into Ea, the Valaquenta notes "The Great among these spirits the Elves name the Valar, the Powers of Arda"
and
"With the Valar came other spirits ... of the same order as the Valar but of less degree. These are the Maiar..."

In the Judeo Christian tradition there are different orders of Angels wit different powers and functions.

Exactly. The Ainur were the greater in terms of spiritual stature and in the hierarchy, and the Maiar were simply the same order of being but of lesser power and "rank", having the tasks of aiding their superiors.

I have recently been delving into greek mythology again, so the first real world example that came to my mind was the division between the twelve Olympian gods and the rest of the gods.

Yes, there were plenty of lesser gods and demi-gods in the Greek pantheon. Interestingly enough, many Greek heroes reached godlike stature and became parts of constellations, which mirrors Eärendil's ascent into the heavens.

In regards to heavenly hierarchy, Dante in his Divine Comedy divided the angelic hosts in much the same order as St Jerome and St. Gregory the Great: Seraphim, Cherubim, Thrones, Dominations, Virtues, Powers, Principalities, Archangels and Angels.

Yes they were both Ainur.

"With the Valar came other spirits whose being also began before the World, of the same order as the Valar but of less degree... their servants and helpers." [Sil. p. 23]

Of the Valar it is said that they are "the Powers of the World" since "their power should thenceforward be contained and bounded in the World, to be within it forever, until it is complete, so that they are its life and it is theirs." [p. 10]

The Maiar were called forth by Manwë and the other Valar, "he called unto himself many spirits both greater and less, and they came down into the fields of Arda and aided Manwë, lest Melkor should hinder the fulfillment of their labour for ever... the Valar drew unto them many companions , some less, some well nigh as great as themselves, and they labored together in the ordering of the Earth and the curbing of its tumults." [pp. 11-12]

Indeed. Like the Archangels would be of the world of Briah [this, the creative world, and below God acts through His ministers] and the other Angels [Angelic orders] of the world of Yetzirah [the formative world]. Each of the four worlds corresponds to a letter of the divine name Y-H-V-H. Going to another Abrahamic religion in islam the wings an angel [malaika, or power as they are called] possess [ch. 35; v. 1] show the number of their responsibilities.

I'm not really sure it's quite the same, although they are lesser. Like there is Hebe who serves the Olympians for example, but it seems for the most part they all do their own thing. The Fates, not even Zeus is above, and remember they had to overthrow their parents and their brethren, the Titans who were the first gods, after Cronus castrated his own father Ouranos before that. There is one real similarity with Poseiden and the gods of all the various waters, the rivers, streams, etc., who are under him. And Zeus is the father of the Gods and Men. Some of the Olympians like Apollo and Ares are his children, not so with the Valar. Hercules ascended to godhood was once a man.

That's all true, and I agree that the forming and the history of the division is very different. But the concept is pretty similar, I think. They're all gods, but some have more power and distinction than others. That's the main parallel I was thinking of.