The unique character of Tisha B'av manifests itself in two distinct ways. Modeled after Yom Kippur, Tisha B'av is essentially a ta'anis tsibbur (a public fast). The Talmud in Pesachim (54b) explains: "Ein bein Tisha B'av l'yom hakippurim ela shezeh sfeiko assur v'ze sfeiko muttar" - the only difference between Tisha B'av and Yom Kippur is that whereas situations of doubt are forbidden on Yom Kippur, they are permitted on Tisha B'av. Accordingly, the chamisha enuyim, the five afflictions that are forbidden on Yom Kippur are prohibited on Tisha B'av as well.
Teshuva (repentance), essential to Yom Kippur, is a central theme of the krias haTorah (Torah reading) on Tisha B'av. "B'tsar l'cha u'mtsaucha kol hadevarim ha'eileh b'acharis hayomim, v'shavta ad Hashem elohecha v'shomata b'kolo" (Devarim 4) "When you are in distress and all these things have befallen you, at the end of days, you will return unto Hashem your God and hearken to His voice."
Tisha B'av however, is not merely a ta'anis tsibbur. The Talmud in Taanis (30a) teaches, "Kol mitsvos hanohagos b'aveil nohagos b' Tisha B'av". In addition to ta'anis tsibbur, Tisha B'av is characterized as a yom aveilus - a day of mourning. This aspect of the day is emphasized in the haftorah, "asof asifem", "I shall utterly destroy them", which underscores the despair, suffering, and aveilus of Keneses Yisrael.
The Meiri (Yoma 78a) explains that because of this additional element of aveilus, Rabbi Yehoshua Ben Levi refrained on Tisha B'av from wiping his face, hands, and feet with a towel - a practice that is permitted on Yom Kippur!
Emphasizing the nature of Tisha B'av as a day of mourning, the Chassam Sofer (Ohr Hachaim siman 157) maintains that even individuals who must eat on Tisha B'av can be called to the Torah and receive an aliyah. He suggests that the obligation of krias haTorah on Tisha B'av is not merely a function of ta'anis tsibbur, but reflects the character of the day as a yom aveilus.
Although we often associate tefilas neilah with Yom Kippur, the Mishna in Taanis (26a) explains that this tefilah is recited on fast days decreed in times of calamity. If so, why is tefilas neilah not recited on Tisha B'av? Rav Solovietchik zt"l explains that unlike shacharis, mincha, and ma'ariv which are independent tefilot, neilah is an encompassing tefilah through which we beseech Hakadosh Baruch Hu to accept all of our tefilot of the day. If an individual failed to daven shacharis, he can nevertheless fully fulfill his obligation to daven mincha. Failure, however to daven any of the tefilot of Yom Kippur, renders tefilas neilah incomplete.
Ta'anis tsibbur in general, and Yom Kippur in particular, are times of kabolas tefilah and we are therefore obligated to recite neilah. Tisha B'av however is characterized as "sosam tefilasi" (Eicah 3:8) - a time of aveilus when our tefilot are silenced, and hence we omit tefilas neilah.
May our taanis and aveilus elicit rachamei shomayim on behalf of Keneses Yisrael.