Tolerated use of the term topology
Yes, I suppose you could, though it might be viewed as a somewhat informal usage of the term "topology".  "Shape" would probably be a better word, as @Raphael suggests.

A more precise way would be to say that these two trees are not isomorphic.

Background: Two graphs $G,G'$ are considered isomorphic if there exists a map $f:V \to V'$ that is a graph isomorphism.  Since any tree can be viewed as a graph, you can consider two trees to be isomorphic if they are isomorphic as graphs.  One can also define a natural notion of a tree isomorphism directly; this happens to be equivalent to the notion of a graph isomorphism for unrooted trees, but is slightly different (and more appropriate to use) for rooted trees.  You can read more about isomorphisms in standard sources.