::jumps in, kind of late to the party::
(This is my first post, so I apologize in advance if I screw something up. And I have lots to say, because I've been mulling it over while waiting for my account to activate.)
I don't think there's any definitive canon answer either way--there's plenty of evidence that Jadis and the Emerald Witch are the same, and there's a lot of evidence that they aren't. (I will admit here that I spent
years being totally convinced that they were the same, and the first time someone questioned it I was totally flabbergasted.)
To start, there's two biggest points against it, for me:
- Jadis is killed by Aslan at the end of the LWW
- Jadis and the Emerald Witch act differently--the Emerald Witch is capable of feminine wiles, so to speak, and Jadis apparently isn't.
On the other hand, Jadis ate the apple in MN, giving her "unwearying strength and endless days like a goddess" (MN chapter 14). And in PC, we get the hag assuring us that "who ever heard of a witch that really
died? You can always get them back" (PC 13), and the rest of the company takes that as a serious threat [someone made an excellent point that, were they one person, Jadis should be underground at this point--but I'm not sure we have a definite timeline there, and anyway we aren't sure if the spell is a "bring her back from the dead" spell or a "locate her" spell or what]. As for her death, we don't actually see Jadis die, do we? We see that Aslan has "flung himself upon the White Witch. Lucy saw her face lifted towards him for one second with an expression of terror and amazement. Then Lion and Witch had rolled over together but with the Witch underneath" (LWW 16), and then we cut to the end of the battle, when the Witch's army know "that the Witch was dead [and] they either gave themselves up or took to flight" (LWW 17). And the narrator never actually says the witch is dead--he says her army *saw* that she was dead, which is a different thing altogether. So I would assume that it's possible that, whatever happened to Jadis at the end of LWW, she could be back again later. And while Aslan might be *able* to kill her, we know he follows his own rules, and the line about her being immortal was written after she apparently died. So I think either explanation fits with canon.
The other thing that gives me pause is that both witches go after Narnia with nefarious plots, but never seem to have plans of expansion. The White Witch, for instance, never bothers to take over Calormen. And I don't remember the Emerald Witch wanting to either (please, correct me if I'm wrong). And if I were an evil witch who knew that anyone who goes up against Narnia invariably winds up having to deal with Aslan, I would probably shelve that plan and take over the rest of the world first, if my plan was simply power. A personal vendetta, on the other hand, might cause me to try for Narnia again and again.
I admit that the White Witch and Emerald Witch have different powers, apparently, but then--so does Jadis in MN. And several thousand years is quite long enough, I should think, to learn different and more complicated magic. And there is the interesting inscription from SC that someone else mentioned.
Anyway, I personally think that this is one of those questions that can't be definitively answered either way, because I think both explanations work within the canon we've been given.
