I suppose it depends on your definition of what fasting actually means, but I tend to rely on the Natural Hygiene definition which has stood the test of time..........
"Fasting----the abstention, entirely or in part, and for longer or shorter periods of time, from food and drink or from food alone………...Dr Herbert M Shelton . D.P., N.D., D.C., D.N.T., D.N. Sc., D.N.Ph., D.N. Litt., Ph. D., D. Orthp."
The dictionary defines a diet as a "regulated course of eating and drinking, a specially prescribed regime. The daily fare, victuals, allowance of food; rations." To "diet" is "to regulate or restrict the food and drink according to a regime; to eat carefully or sparingly. To take food; to eat."
"Fasting, as we employ the term, is voluntary and entire abstinence from all food except water. "Little driblet meals," says Dr. Chas. E. Page, "are not fasting. There should not be a mouthful or sip of anything but water, a few swallows of which would be taken from time to time, according to desire." We do not employ the word fasting to describe a diet of fruit juice, for example."
Fasting has become a word of ambivalence & ambiguities which necessitates clarification, and which the early Natural Hygienists defined more than adequately for us.
But there is no doubt in my mind (and that of other experienced members in this forum, such as Fonty) that a fast is to abstain from all forms of nutrition except water.
A juice fast is really no more than a juice diet (although very beneficial) because you are partaking of nutrition from external sources, whether in a reduced calorific form such as liquid, or a solid food reducing diet.
I shall leave the reader to make up their own mind.