The word diet comes from Greek and means nothing more than way of life. A special way of eating is described by this word, which means the meaning has changed since Hippocrates’ time. Now it means that a special selection of food is eaten during a longer period of time. The intake of nutrients such as fat or carbohydrates, but also protein, is reduced during a diet or at least should be.
So, a diet describes a special form of nutrition, whereas fasting compared to a diet limits nutrient intake in general.