I mean, I don't want to get too far into my OTHER favorite purple-clad Gotham vigilante (she has her own appreciation thread here that needs love!
http://community.comicbookresources....s-Appreciation). But short version: yes, she's the same character. Like Steph and Cass, she was erased in the n52, but it was much, much more offensive, because they wrote a Huntress miniseries teasing fans that she was still alive, but then it turned out it was Earth 2 Helena Wayne. (I'm still mad.) Then Tim Seeley introduced her at the end of Nightwing/beginning of Grayson as the head of Spyral's academy for girl assassins, and after he left Grayson, he brought her into Nightwing for an arc. He's also bringing her into Hellblazer for an arc (I'm probably going to buy that as well, since Seeley writes a pretty great Helena, I think.) I have no confirmation on whether Seeley's going to use her in Green Lanterns - I'm just making a joke based on his previous work.
After Batman Eternal, when Steph and Tim flirted in the very last issue, I was really bummed that not even Batman and Robin Eternal really did anything with that relationship. I'm really glad Tynion decided to put them back together, but I wish he'd done it in Batman and Robin Eternal - have them get closer in that series - instead of just surprising us in the second issue of Tec.
I'm still really unsure of why they changed The Button. That whole miniseries was so pointless without the reveal that Tim was alive.