If you are comparing the smoothness of two thing, "smoother" refers to the one that is more smooth.
For instance, if you are a carpenter, you might sand wood to make it smooth (so it is not rough, and does not have splinters). It is also used in describing alcoholic beverages. The smoother beverage "goes down" more easily. It is less harsh. It has a milder taste.
You can also use the word to describe the texture of food in your mouth. A food with a creamy quality (like yogurt or pudding) might be said to have a "smooth" consistency.
In my opinion, traditional, full-fat yogurt has a smoother consistency than Greek yogurt.