Today belongs to the this new year. That is why there’s an apostrophe there. Same with new year’s eve. I’m not really sure why the case is different for Christmas eve though.
From what I have read it seems likely that NYE and NYD refer to the actual occurrence of that day, whereas Christmas eve refers to the generic day. That seems quite a lot like bullshit to me though.
Oh well, hope you’re all having a happy one. 🙂