Difference between UCB1 and UCT
As the authors state in the introduction to their paper, UCT is an application of UCB1 for a specific problem:


  The main idea in this paper it to apply a particular bandit algorithm, UCB1
  (UCB stands for Upper Confidence Bounds), for rollout-based Monte-Carlo planning. The new algorithm, called UCT (UCB applied to trees) described in Section
  2 is called UCT.


It's not the algorithm but the particular application which is new.