Traditionally, Greek yogurt involves straining regular yogurt, removing the liquid and leaving a thicker, more concentrated yogurt that has about 2x as much protein as the original yogurt. This makes for a great snack if you can find a brand that isn't heavy laden in added sugars. I have found Yoplait 100calorie and Dannon Light&Fit Greek to be the two lowest in sugars and still have flavor.
Regular yogurt tends to have more calcium than Greek yogurt. Due to the straining of the liquid (whey) from regular yogurt to make Greek yogurt, Greek yogurt loses a lot of its calcium content. If you are depending on your yogurt to be your main source of calcium for that day, I would go with a non-fat regular yogurt.
No matter your decision, be sure to add your own fruit and flavorings instead of buying the yogurts that are full of fake-fruit or toppings.