The Gemara in Taanit 12b seems to say that there’s no fast like the fast of Tisha B’Av. Tisha B’Av then is the quintessential fast. Shmuel, or in another version, Rabbi Yirmiya bar Abba said, “There is no Public Fast in Babylonia except for Tisha B’Av alone.” How so? In what way is Tisha B’av unique, superior to other fasts? Rashi on the spot mentions two notions of stringency, not wearing shoes and starting the fast at night.
However, the Gemara in Pesachim 54b presents a debate as to whether Tisha B’Av is the only true fast (Shmuel) or that it is not a Public Fast (Rabbi Yochanan). The Gemara suggests several other possible unique features of Tisha B’Av. a. That one must fast even during its twilight time. b. That pregnant and nursing mothers must fast as they do on Yom Kippur (speak to your local MOR and doctors) whereas they needn’t do so on other fasts. c. They considered the notion that people shouldn’t work on Tisha B’Av though that is more of a local custom. The Gemara then entertains the option (d.) that Tisha B’av is unique in that one may not even dip a finger in water (unless one is very dirty). All of this is codified into common practice today.
Rabbi Yochanan, however, said that Tisha B’Av is not a Public Fast day. The Gemara suggests two ways to understand what he meant by this. Did he mean it is not a Public Fast day in respect to not saying the prayer of Neilah as we do on Yom Kippur, or in respect to not adding the 24 blessing version of Shmoneh Esreh which was said on true Public Fast days of old? It is left unresolved. The Ramban in Toras Haadam seems to think both ideas are true.