A bit slow, but just noticed my Moto G has two apps as above, which are broadly similar. Was one supposed to supersede the other ?
Gallery is the Motorola App, Photos is tied into Google+.
Just disable Google+ and it'll go away.
Shouldn't even need to do that anymore, Photos and Google+ separated a while back
https://play.google.com/store/apps/details?id=com.google.android.apps.photos
Photos is a Google app.
Gallery is a stock Android app.
OP didn't say "Motorola Gallery". My mums Moto G doesn't have that one preinstalled, just the stock Gallery.
Motorola gallery is the stock gallery app - its not called Motorola gallery anywhere other than the play store (apps list it shows as gallery), but the icon is the same and I bet if you open the above link in play store on your phone, it will show as installed.
It doesn't. It says its incompatible. The icon and screenshots are completely different to the Gallery app.