Generally, when observant Jews think about fasting, they think about the dry fasting done on the 9th of Av or Yom Kippur, in which we neither eat nor drink. This is related to the idea of rising above the physical/material plane of existence.
In the context of a one-day fast, or even a two-day fast, dry fasting is doable, but also puts some stress on the body.
Conversely, in the context of making a tikkun over past transgressions, the number of fasts prescribed in Torah is often many more days than simply a day or two. See for example the references in the Tanya in Igeret HaTeshuvah at the end of chapter 1 to Sefer Rokeach and Mishnat Chassidim and also in chapter 3 there.
Medically speaking, water fasting, meaning abstinence from eating, is something that can be done for many, many days consecutively. The world record for fasting is over a year. However, a dry fast (abstinence from both eating and drinking) can only be survived for three to five days. The abstinence from water is the critical factor.
Does the Torah make a distinction between types of fasts? The Aramaic word for fast is תענית from the Hebrew ענה. The Hebrew root has a connotation of to respond or to answer (as in answering for improper actions) and also to deprive, or to delay, or to submit/become humble or to become poor. All of these relate to the idea of depriving oneself of food in humility and an act of submission to G-d's will.
The consequence being that one burns their excess body fat, which is compared to burning the fat of an offering on the altar brought in the Temple, like is mentioned in the Tanya for example.
So the focus seems to be about the burning of body fat, which relates to the eating of food only.