Is the number of iterations in gradient tree boosting just the number of trees?
Your first interpretation is correct. One base learner will be added per boosting iteration/round and that is probably what people are referring to when talking about iterations. 

From wiki:


  One natural regularization parameter is the number of gradient
  boosting iterations M (i.e. the number of trees in the model when the
  base learner is a decision tree).


Iterations take place in other parts of the algorithm, for instance in the gradient descent, but I don't think that is what is discussed if it is simply referred to as "iterations".

This was really helpful when I was trying to understand GBMs