Partially fasting is like being partially pregnant. You either are or you aren't. The purpose of true fasting is to shut down the digestive system so the energy normally used in digesting food can be diverted to cleansing accumulated wastes and allowing the body to heal. Weight loss is simply a part of fasting, at least in the first dew days.
While I agree that there is really no such thing as a partial fast, eating a few calories a day does stimulate digestion and may actually result in more weight loss than fasting alone. The stricter the fast, the more rapidly the body goes into starvation mode and the metabolic rate slows down to the point where very little weight is lost.
Most of what is being practiced on this forum is extreme dieting, very few here will experience the cleansing and healing effects of true fasting as long as they use coffee, tea, artificial sweeteners, any solid food, or do off and on fasting.
Still its all a matter of semantics, and as long as they members are reaching their goal of rapid weight loss, words really don't matter. Most of the fasting forums are dominated by those who wish to lose weight.