You have separate Rune Pools when you join different cults.
So, for example, Orlanth gets Tame Bull from Barntar, so an orlanthi could cast tame Bull with his Orlanth rune Pool, he doesn't have a Barntar Rune Pool. Now, if he also wanted to join the Barntar cult, as he is a farmer through and through, he would get an Orlanth Rune Pool and a Barntar Rune Pool. He could cast Tame Bull from either pool, as Tame Bull is available to Orlanth and Barntar.
A better example would be Orlanth and Yinkin. Yinkin provides Identify Scent to Orlanth Adventurous, so a member of Orlanth Adventurous can use his Orlanth rune pool to cast identify Scent. If he joins Yinkin then he also gets a Yonkin Rune Pool, which he can use to cast Identify Scent and the other Yinkin spells, such as Catseye or Claws. Since Orlanth gives Yinkin Shield, the cultist can use either Orlanth Rune Pool or Yinkin Rune Pool to cast Identify Scent or Shield.