Uglúk leads the Uruk-hai who capture Merry and Pippin after the breaking of the Fellowship. He is an Orc captain serving Saruman and commands the large, specially bred Uruk-hai sent from Isengard to intercept the Ring-bearer’s companions.
After Boromir is killed defending the hobbits, Uglúk’s force seizes Merry and Pippin and begins driving them toward Saruman’s stronghold. The group includes Uruk-hai from Isengard as well as other Orcs, creating conflict over whether the prisoners should be taken to Saruman or delivered to Sauron’s servants.
Grishnákh leads the opposing Mordor-aligned Orcs, not the main Isengard contingent. Lurtz is a film-created Uruk-hai captain who kills Boromir in Peter Jackson’s adaptation, but he is not the commander identified in Tolkien’s book. Saruman himself directs the wider mission but does not personally lead the capture party.