I've played Skyrim through several times (as a good guy and a bad guy) and while I'm waiting for the next game, I decided to play Oblivion. I'm really impressed with the continuity between the two games. But one thing is really bugging me; in Skyrim, Peryite is the Daedic prince of order and tasks, however in the Shivering Isles expansion of Oblivion, Jyggalag is the Daedric prince of order. What's up with that?
In Jyggalag's case, I think that "order" refers to logical deduction and determinism. This is not unreasonable considering that his Great Library contained formulae that allowed him to predict all events before it happened.
According to the Librarian, Dyus:
The great library was the height of logic and deduction. Contained within its walls were the logical prediction of every action ever taken by any creature, mortal or Daedric. Every birth. Every death. The rise of Tiber Septim. The Numidium. Everything. All predicted with the formulae found within Jyggalag's library.
When the jealous Daedra cursed Jyggalag to live in opposition to all he stood for, they made him the Prince of Madness which is the opposite of logical deduction. In Shivering Isles, Dyus mentions that Sheogorath burned the library because it was the anti-thesis of his new beliefs in personal choice:
When Sheogorath discovered the library he had it burned, insisting that it was an abomination and that personal choice defied logical prediction.
Thus, I think that the Lore strongly suggests that Jyggalag is the Daedra of Order in the sense of Logical Deduction and determinism.
Regarding Peryite, there are two main in-game sources of information on the Daedra:
Firstly, we have On Oblivion by Morias Zenon
...Molag Bal elects the employment of other daedra, and Boethiah inspires the arms of mortal warriors. Peryite's sphere seems to be pestilence, and Vaernima's torture.
In preparation for the next instalment [sic] in this series, I will be investigating two matters that have intrigued me since I began my career as a Daedra researcher. ...
Secondly we have The Book of Daedra
Peryite, whose sphere is the ordering of the lowest orders of Oblivion, known as the Taskmaster.
Neither of them indicate that he's a Daedra of "Order" or that "Order" is part of his sphere. Rather
The Book of Daedra makes him sound more like a foreman who manages and "orders" the lesser Daedra around. This is the reason why the primary sources are quick to elaborate that whatever ordering Peryite does is more akin to that of a "Taskmaster".
Notice that in the original text, they add emphasis to the fact that he's a "Taskmaster" by capitalizing the word, but do not do the same for "ordering". This is done to illustrate what his main function is and how he's different from Jyggalag.
Thus, even if we choose to believe that Peryite is a Daedra of Order, it seems clear to me that his sphere of "Order" is distinct from that of Jyggalag's.
Of course, if this is still unacceptable, we could take the cop-out route and simply claim that Peryite took over his Lord of Order position after he became the Prince of Madness! Since Jyggalag was cursed before recorded history, this explanation isn't contradicted by any in-game manuscripts.
Put simply, this is a case of the everso common homonym in the english language.
Peryite is a foreman, a person who orders(gives a command) around his daedra and micromanaging his sphere and the rest of Mundus with minions.
Jyggalag, is the master of Order(structure, sequence, pattern, method, Relativity) and he is the all knowing recorder on time-space and existence.
This sadly is why he was cursed... Hermaus Mora didn't like the fact that Jyggalag could see his oh so valuable information so he banded the rest of the daedra against Jyggalag by making them think that they were in danger of having their sphere conquered or , in the case of Bolag Mal that they could enjoy messing with another prince. So he was cursed... then the rest of the story is known through playing the shivering isles DLC Enjoy ;)
Peryite is more of the "balance/equality in the universe" type of Order. Jyggalag is more of the straight-lines, grey, "boring" type of Order
From what I understand(and I unfortunately have no sources for this; this is merely conjecture) Peryite is more or less Order in the form of Bureaucracy; he manages the lesser planes of Oblivion.
Jyggalag is ruler of the PLANE of Order. His whole being is dedicated to Order in and of itself, while Peryite simply uses Order as a management tool, trying to make Order from the Chaos that must stem from managing numerous planes of Oblivion.
Hope this at least gives another perspective. ^_^
Due to both information gained from Dyus (as well as Dyus's personality) and the descriptions of Peryite as a 'Taskmaster,' I believe the difference to be as so:
Jyggalag represents the concept of predeterminism and the ideas of logical prediction and a sort of Holmesian Deduction (different from Herma-Mora, who keeps ancient and secret knowledge).
Peryite represents Order in the sense of the managing and 'ordering' of the different daedra (as the Prince of Pestilence, he might be described as head of the 'dirty work' in the Planes of Oblivion).
In this sense, you could differentiate the two be saying that Peryite keeps order among the daedra while Jyggalag maintains Order in general.