So I read this: http://www.imperial-library.info/content/alduinakatosh-dichotomy
And the author concluded that Akatosh and Alduin were in fact one, contrary to nord beliefs. He just says that the story about Alduin as a world-eater is just an oral story that isn't reliable at all, but after the return of the Dragonborn in the 4th era we know that these stories are real. We face Alduin, go to Sovengarde where he devour souls and even travel through time to witness the Drago war. So Alduin the world-eater is real. But is he another person than Akatosh, or is Akatosh the world-eater? Or is Alduin some pantheon of Akatosh? I think I can remember someone saying that Alduin is the firstborn of Akatosh as well.

There is another book that says the two dragons are different. and i believe that Akatosh and Alduin are different.

Alduin is the first-aspect of Akatosh.

http://www.uesp.net/wiki/Lore:Alduin_is_Real

Before the game was released there were on the forum roughly two camps of thinkers.
Scholarly people that used long theses to explain why in a mythical sense they were one and the same creature, using words like enantiomorph, mytho-poesis and fractal. And literal-minded people that basically said: They are not the same, because they are named different and come from different cultures.

I believe that these two books are a little joke Bethesda made on that discussion, which got quite heated at times.

I was in the first camp at the time, but it turns out that the second one was more right than I was.

Alduin appears to be a subgradient of Akatosh. Dragons make several references to Akatosh being their father and there is a bit of apocrypha that states that Alduin split from Aka.
Since this happened after creation it would make Alduin Ehlnofey and so I while I was wrong, in a way so were they and a person can have peace with that

He's Alduin and Akatosh, in the way that the nerevarine is him or herself yet also Nerevar.* While you can get the two of them in the same room and they can think and act separately, at their core they are aspects a single being, which is Time. The Akatosh of the Imperial Pantheon, even though he was retroactively created by humans after Alduin was banished into THA FYOOO-CHURRRR!!!!! is representative of "time as thing itself," and therefore eternity. Alduin is representative of "time as that which ends other things."

Go read the monomyth, it has foreign gods interacting, we just didn't emphasize the relevant passages before release.

*This is not truly anything like that, but it's a lie people can understand and doesn't take like four paragraphs.

Some time before release, MK said something interesting, something about how the Nine (which would have logically included Akatosh) always ensured there was a loophole to ensure Alduin doesn't devour the world. This was before we got any real evidence that Alduin was anything other than the Nordic aspect of Akatosh/Auriel.

Edit: And frankly, those who believed that Alduin and Akatosh weren't the same before this wouldn't have used it as evidence when it was posted.

Replace the loophole or walkabout with elder scroll, Akatosh with Ruptga and Alduin with Satakal, then you got a possible answer.

I like to think Akatosh would be slightly harder to kill. And there are other books with conflicting ideas. Besides, wouldn't being technically "dead" and bound to Mundus prevent you from actually appearing in your full glory? If anything I'd contend that Alduin is either an avatar of Akatosh, or Akatosh's child.

Gods are beyond our mortal minds' ability to comprehend. Especially Akatosh/Auriel/Alduin/Aka/etc., who not only exists outside of time, but is time itself. Aka is Alduin, but is not as well, because our brain can't understand two beings being the same being but not being the same being because one is an aspect of another...ack! Aka wishes to continue this kalpa, while Alduin wishes to devour it. Because of non linear time during the Dawn Era, all myths are true (for the most part). Akatosh is the world eater, but only because Alduin is the world eater. It also helps that Akatosh is said to be insane/schizophrenic.

EDIT: Inb4 Alduin mantled Akatosh son of Aka son of Anu.

There's Aka, then there's Aka.

Don't get them confused.

From TIL:
There's also this:

Song of Shezzar in the Monomyth says parts of that only prettier, where "Auriel," who we all know to be "Akatosh," is in conflict with Akatosh based on their disagreement over whether the sacrifice to make the world was a good thing. That corroborates the "could" of the mirror-brothers in conflict.

Alduin refers to himself as "firstborn" of Akatosh at the conclusion of "Alduin's Bane." What would "firstborn" mean in the context of an Aedra?

Largest fragment me thinks.

What do you mean by "largest fragment?"

Perhaps he is the first being created by Akatosh during the Convention. And by extension, the strongest.

First interpretation by degenerated et-Ada.

Alduin, the time dragon as a firestorm tearing through the sky to end Lorkhans endeavor. (the destroyer)

In contrast to the time dragon as the spirit that enabled and gave purpose to the life of the other spirits (the guardian/Akatosh) or the time dragon as a saviour that will liberate from a falsely adverised endeavor (the saviour/Auriel).

Being the first, he presumably would have seen most of the Creation and the gradual degeneration/dilution of the Aedra. Thus if anyone knew how to reverse it, it would be him.