Oh snap. I'm so sorry. You're right!
They're the same thing. Issue one of "I am Gotham," Finch and King's collab for the ACTUAL beginning of Batman's Rebirth "reboot."
I was confused because in the iTunes Store, the Batman Day 2016 comic is FREE while the regular edition (with a different cover but the exact same shit in it!) is $2.99. I spent that bread TWICE on getting a digital and paper copy of the non-Batman's day one, so it kinda pisses me off that it'a fucking FREE if you get it with a different (lamer) cover! Only reason I bought the digital was for readability. Would have grabbed that free shit if I could.
Also, I covered two Batman Day events at local libraries and I swore they had free (or $0.26 at comic shops) Batman Day Comics with the cover of the one you have, and I swear they were mostly for kids coloring activities.
But yeah, I just grabbed the free one and it's the same exact thing I spent money on.
My bad. Sorry. Carry on.