As you most likely know, Emma was the younger sister (and a major plot point causing the actions) of Silverfox in Wolverine: Origins.
Then, in X-Men: First Class, as if our memory was supposed to be wiped cleaner than Wolverine's, a much older Emma Frost plays a very large supporting role.
Virtually the same character, the Wolverine version is supposed to have never happened according to Fox Studios.
I have a couple explanations as to why this is, though I assure none are true but it eases my mind to think that Fox does care about the franchise (and fans) a little.
1) Although Wolverine: Origins the game hints that Wraith, not Azazel, is the father of Nightcrawler, it is not cannon to the movie series. Understanding that, and seeing First Class in theatres, I can surmise that Mystique and Azazel bond whilst helping create the original brotherhood and she becomes pregnant with Kurt (throw Magneto in there for a love triangle).
That leaves Emma and Riptide (who was never named within the movie). Fox studios changes anything they want in these movies so why not make those 2 parents of Silverfox and Emma. Thus explaining the similarities in looks and the same name. The darker Silverfox could have taken after her father. The timeline fits fine, too.
2) Shaw, who was very similar in his "mad scientist of genetics" personality to Sinister. Sinister was always conducting experiments and cloning and what not. Who's to say Shaw didn't clone Emma (just in case). The younger Emma of Wolverine may not have been a real sister to Silverfox and may be 1 of many Stepford Cookoos.
This, as crazy as it sounds gives me peace of mind, untrue or otherwise.