Frequently tunes are played three times through. But just as often, a session will play a “set”.
A common format for a set is three tunes of a similar type, but in different keys, each played 3 times.
Generally a set within a session will focus on one type of tune: reel, jig, etc. Bands will often arrange a set that includes both reels and jigs. But, this format is rarely found during a session.
Occasionally airs or tunes by Turlough O’Carolan or Neil Gow may be played during a session. These are generally not grouped into a set, but stand alone.
Even less frequently a song will be offered during a session. Often the song is presented as a solo effort by a very strong singer. The traditional free style is called sean nós. See this link for details about this song style:
Sean nós singing is important to hear. It is this style of singing that strongly influences both the playing of the pipes and the ornamentation of Irish music.