If there's no creed patch and it's the same size as the other one, it's fake. Period.
Just FYI,
Coach doesn't write style numbers on the outside of their boxes - they don't write ANYTHING on the outside -, and that's not a standard Coach box either. And didn't the wording "
Women Coach Alligator Tote Handbag" sound a bit odd? That's how thousands of listings for Chinese fakes often start.
In addition, the inside zippers are different, even the zipper pull on the fake looks like cheap Mystery Metal. There's NO photo of the inside and no mention of the serial number, and with a bag that's supposed to be a Limited Edition they should at least have posted photos of the creed patch.
If it doesn't say Coach anywhere on or in the bag, it's a knockoff that they're passing off as a Coach. And technically if there's no Coach name or logo on the bag, it's not even counterfeit, it's just a scamming seller trying to rip someone off.
Contact them and demand a full refund including your shipping charges, and start a SNAD claim with Ebay at the same time. Mention to Ebay that you own the verified GENUINE version of the bag and you can send comparison photos showing where the differences are. Don't mention "counterfeit", just say the bag was sold to you as a genuine Coach but it's not.
And please, next time ask here first, and don't ever bid on anything without a clear creed photo.