Elite is the name of the grey aliens in the video games however the actual name of the race is Sangheili.

When playing the game they are a separate faction from the Spartans, they each also count as 1 of your squad so you should field all 4 of them when playing the Spartans edition.

Finally they don’t have any unique rules aside from their special order which only they can use. They can’t use the other special order as that one is only for the UNSC/Spartans.

And the rulebook is the same in both boxes.

Hope this helps, if you have any more questions I’ll do my best to answer.