divines can be killed btw, deadra can only be banished and thus they can return eventually, so in godly terms they are more divine than the divines XD
Killed is a relative term in both cases.
As another poster said, the absence of a god causes someone to fill that space; Talos the mortal became Lorkhan the divine, and the hero of Cyrodiil became Sheogorath. It's more a case of a mortal and his/her body being filled with the divinity.
But Sheogorath didn't die himself, he merely became Jyggalag. And Lorkhan didn't die, he pulled an Osiris and became not just the God of Mortals, but the Mortal God, and rules over the Dreamsleeve (Sovngarde IS the Dreamsleeve; Sovn = sleep, Garde = vessel). Both transformed, and granted their divinity, and all the titles that went along with it, to heroic mortals.
In a way, all of the Divines can be thought of as merely titles, except at present Ehlnofey or something older fill those slots. All Aedra and Daedra mean are whether that aspect of divinity is involved with creation or destruction in Mundus. Thus Trinimac became Malacath, and thus the good-aligned Azura and Meridia are both Daedra in spite of being helpful to mortals.
EDIT:
right but truly you didnt become a god though on shivering isles you just took over the realm right? you could still die and gained no real power or invulnerability, daedric princes are true gods invincible moreless, however they are different from aedra, as they cant enter tamriel at all, they cant even speak to anyone directly, unlike daedra that some can enter tamriel as they please, like sanguine, and sheogorath, and a couple others, mehrunes but he was the rightful ruler of tamriel in the merethic era i believe but was cast out of his realm and tried to regain entry from the oblivion crisis. so daedra can enter the realm and speak directly to people, but the divines cant, are the divines even in comparison to the daedra, im thinking the daedra could create and transcend a more powerful new prince than the divines created talos, perhaps.
No, you took on all of His powers. Sheogorath of Skyrim makes references to being the Hero of Cyrodiil, and even to
browsing the Elder Scrolls forums (in the form of referring to the "fish stick, a very delicate state of mind"). Also, try hitting him next time you do his quest.