Seemingly following in Google's footsteps, Motorola has released one of its phones' core applications on the Play Store today, in the form of Motorola Camera. Unlike Google's apps, though, it doesn't seem likely the Motorola Camera app will be making its way onto non-Moto devices - it's only compatible with the Moto X.
Likely, the app is simply a way for Motorola to quickly update the camera software on its smartphones without having to develop its own app updating system, similar to the practice it began by putting Touchless Control on the Play Store. You can probably expect the Moto Camera app to expand compatibility to the DROID line of phones at some point, but I wouldn't bet on it going much further than that.
This app will update the existing camera app on your Moto X, and claims to increase viewfinder brightness, allow quick capture to be enabled under more enterprise IT policies, and squash some bugs. You can get it, assuming you have a Moto X, at the Play Store link below.