The difference between Greek yogurt and regular yogurt is really a matter of straining and process. Greek yogurt and regular yogurt start with the same ingredients, which is yogurt. And you can either get it with cow's milk, you can get sheep's milk or you can even get coconut milk yogurts now.
And what happens with Greek yogurt is that they strain the yogurt more thoroughly, and that removes more of the liquid, more of the whey and more of the lactose. So what you end up with is more protein in a smaller amount of calories and less sugar in the Greek yogurt. So you can eat the same amount of Greek yogurt as regular yogurt but you're getting more nutrition out of it in the same amount of calories. Maybe even less because they've even removed most of the sugar as well.
So some people find that they digest Greek yogurt better than regular yogurt because there's less lactose in it. Now for all you dairy-free people out there, the great news is that there's fantastic coconut milk Greek yogurt out now. So you can get great dairy-free Greek style yogurt to help you with any dairy-free issues that you have.