Akatosh is not Alduin.
Akatosh is the living representation of a god. Alduin is an actual dragon which we've never seen.
No, Alduin is Akatosh is Auriel. Also, Akatosh is nothing more than a political move, the god of time reinvented when Alessia became the first emperor of Cyrodiil. Before Akatosh, the only version perceived of the god of time was against Mundus as Auriel and the world devourer Alduin. The mer saw the god of time as Auriel, the dragon time god who fought for the mer, fought against Lorkhan, and is against Mundus. The nords saw the god of time as Alduin, as a world devouring dragon, and favored by the mer. All of this happened during the Dawn Era, when time wasn't linear. Once time became linear, the events that happened somehow had to fall into place, and as such, the different perspectives became the god of time, creating different personalities of the time god.
But, in order to understand the gods, you must realize that belief shapes them. This is where Akatosh comes into play. He was a political move, created by Alessia in order for the former slaves to hold onto their merrish religion, without pissing off the nords who helped liberate them. Through the power of belief (and the intervention of the Selective) the god of time became Akatosh, the preserver and good guy everyone here knows. Because of the power of belief, there are now 3 aspects of the god of time, who is the same being.
Lets look at another god who has 3 different perspectives, the god of space and the creator of Mundus. This god goes by the names Lorkhan (mer), Shor (nord), and Shezarr (Cyrodiil). Before Alessia, it was just Shor and Lorkhan. The mer saw Lorkhan as a trickster who robbed everyone of their coolness, awesomeness, and immortality with the creation of Mundus. As such, he was punished by Trinimac and had his heart removed. Then comes Shor, the god of space who created Mundus as divine mercy. The purpose of Mundus was to help mortals reach individual ascension, to become something greater than the gods were. This is something Vivec heartily agrees with. And then there's Shezarr, the Cyrodiilic version created as a way to make a Shor-lite.