Difference between UCB1 and UCT In Bandit Based Monte-Carlo Planning by Levente Kocsis and Csaba Szepesvári (2006) they propose the UCT algorithm which is derived from the UCB1 algorithm. 

UCB1 algorithm:
$$X_j + \sqrt{\frac{2\ln n}{n_j}}$$

where $X_j$ is the average reward for machine $j$, $n_j$ is number of times $j$ has been played and $n$ is the entire number of games played.

In comparison, UCT is
$$\frac{W_i}{n_i} + c \sqrt{\frac{\ln N_i}{n_i}}$$
where $\frac{W_i}{n_i}$ is  win:lose ratio (the same as $X_j$),
$c$ is temperature parameter, which is often set to $\sqrt{2}$ (so they just put it in front...)
and $\frac{N_i}{n_i}$  is number of total games played for parent Node / number of games played for the corresponding node, which is the same as $\frac{n}{n_j}$.  

So what's new here?
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.