No. I don't think that's what I mean. With a burst, they all show up in gallery as separate images. I am talking about when a photo has a star in the bottom corner which, when you click on it, it asks you which version to keep.
I believe that's a Moto X 2014 feature called Best Shot and as far as I know, it's just automatically done and there's no way to toggle it off. I'm not even sure what triggers it because I've only had it do that on my phone a couple of times. I think it may be triggered more often if you take portraits like when somebody blinks when you snap the picture and it'll automatically show you a picture immediately before and after the shot that you took, so you can choose the best shot.