Generally a Mussar Vaad provides a more intense and personal level of engagement with an eye to self improvement, thus it usually consists of a small group of students.
A Mussar Vaad can take many forms. It can take the form of a classic "shmuess"- lecture, which is given traditionally by the Mashgiach or Rosh Yeshiva of the yeshiva which focuses on either a particular idea or sefer. However, it differs from a shmuess /shiur in the sense that it is most often a weekly lecture that is built on the previous week's topic with an eye to further deepen the understanding of the topic at hand. This can be seen from the sefarim of Rav Shlomo Wolbe in the Alei Shor which features such weekly vaadim recorded for posterity.
The participation level of a Vaad can also differentiate it from a regular shiur/lecture. Normally asking questions in a regular shiur would be frowned upon. However, in a Vaad, questions can be encouraged to further the discussion. Furthermore, in a Mussar Vaad, when focusing on one topic or midda, ie. anivus, the lecturer can leave the group with a challenge aimed to perfect that midda, and generally the following week the attendees can discuss their triumphs or failures with the challenge given. (This I personally witnessed from Rav Yechiel Perr)
There is also a rotating Vaad, in which the attendees of the Vaad give over the topic on a rotating basis. Sometimes with the switching of the speaker there is also a switching of topics.
Most notably, in the Lithuanian Yeshiva of Novardok they had instituted a very unique type of Vaad, which diverged greatly from other Mussar yeshivos in Lithuania (ie. Slabodka, Kelm, Telz etc.) in something called the "Birzeh" in which students would break up into small groups and critique each other's decisions/characteristics with an eye towards sharpening each other's eye towards self betterment. This is the most intense form of a Vaad and is not considered the norm among mainstream yeshivas. (As heard from Rav Yechiel Yitzchok Perr)
The word Vaad means "commitee" or "council". The reason why it is called a Vaad is due to the primary focus of it. The Vaad attendees desire counsel and insight into how they can further their growth and development, and seek that council from either the main lecturer, or his fellow peers on the personal level which is fostered throughout the Vaad.
Many of this I know through my exposure to Yeshivos that place an emphasis on learning Mussar.