The prophets instituted four fasts after the destruction of the First Temple, the gravest of which is Tish'a B'Av, for that is when the Temple was destroyed These fasts were instituted along the lines of Yom Kippur, which lasts an entire day and contains five prohibitions. When the Second Temple was built, these fasts were annulled, and they became joyful holidays. And when that Temple was destroyed, the four fasts returned to their original status.
After the period of harsh decrees ended and a new era began, in which the Temple was still in ruins but evil decrees no longer plagued us, the Sages determined that the law of three of the fasts – the tenth of Tevet, the seventeenth of Tammuz , and Tzom Gedalyah – depended on Israel's will: “If they want to fast, they do so; if they do not want [to fast], they do not fast.”
On Tish'a B'Av, however, we are obliged to fast under all circumstances, because many tragedies befell the Jewish people on that day, including the destruction of both Temples. Even when times are tranquil, its status is not dependent on Israel's will. Rather, as long as the Temple sits in ruins, we must fast on that day, as the prophets enacted (Rosh HaShanah 18b).
This is the fundamental difference between Tish'a B'Av and the minor fasts. Our obligation to fast on Tish'a B'Av is based on an institution of the prophets; therefore all the laws of the fast apply in their entirety. On the minor fasts, however, our obligation is based on custom - because [all of] Israel agreed to fast [on these days], until the Temple is rebuilt - and from the very outset, the accepted custom was to treat them more leniently than Tish'a B'Av
There are three halachic differences between Tish’a B’Av and the minor fasts:
Tish’a B’Av lasts an entire day, from sunset until the emergence of the stars [the next day], while the minor fasts last only during daylight hours – from daybreak until the emergence of the stars.
On Tish’a B’Av, we are forbidden to do five things:
eat and drink
wash ourselves
anoint our bodies
wear [leather] shoes, and
engage in marital relations. On the minor fasts, however, we are only forbidden to eat and drink.
Only sick people are exempt from fasting on Tish’a B’Av, whereas pregnant and nursing women, as well, are exempt from the other fasts.
In general, the fast of Tish’a B’Av is equal to that of Yom Kippur, for any enactment the Rabbis made regarding Tish’a B’Av was modeled after the Torah’s commandments regarding Yom Kippur. Therefore, Tish’a B’Av has the same five prohibitions that are mentioned in reference to Yom Kippur.
Nonetheless, since the fast of Tish’a B’Av is a Rabbinic enactment, its laws are more lenient in two major ways:
The Rabbis did not require the sick to fast on Tish’a B’Av. In contrast, someone who is ill on Yom Kippur must fast, unless doing so would put his life in danger.
In situations of doubt, one should act strictly on Yom Kippur, but one may be lenient when it comes to Tish’a B’Av. For the rule is, when in doubt regarding a Torah law, one should be strict, but when in doubt regarding a Rabbinic law, the halachah follows the more lenient opinion.
However, Tish’a B’Av is more stringent than Yom Kippur in a certain way. On Tish’a B’Av, we are obligated to mourn. Therefore, we sit on the floor, refrain from greeting one another, darken the room at night, and limit our Torah study to sad topics. On Yom Kippur, in contrast, we are obligated only to deprive ourselves, but besides the five afflictions, the day is considered a holiday: We wear nice clothing, sit on [regular] seats, sing songs, exchange greetings with one another, and of course, engage in Torah study with no limits. (Unrelated to self-affliction, one is forbidden to do work on Yom Kippur, in accordance with all the laws of Shabbat.)